ITP001 Axioms: ITP144^5.ax


%------------------------------------------------------------------------------
% File     : ITP144^5 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 set theory export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : iterate^2.ax [Gau20]
%          : HL4144^5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  362 (  18 unt;  11 typ;   0 def)
%            Number of atoms       : 13724 ( 412 equ;   0 cnn)
%            Maximal formula atoms :  204 (  37 avg)
%            Number of connectives : 21151 (  76   ~;   5   |; 416   &;19208   @)
%                                         (  49 <=>;1397  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   40 (  15 avg;19208 nst)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   82 (  81 usr;  73 con; 0-2 aty)
%            Number of variables   : 1847 ( 216   ^1573   !;  58   ?;1847   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Eiterate_2E_2E_2E,type,
    c_2Eiterate_2E_2E_2E: $i ).

thf(mem_c_2Eiterate_2E_2E_2E,axiom,
    mem @ c_2Eiterate_2E_2E_2E @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).

thf(tp_c_2Eiterate_2EFINREC,type,
    c_2Eiterate_2EFINREC: del > del > $i ).

thf(mem_c_2Eiterate_2EFINREC,axiom,
    ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) @ ( arr @ A_27b @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ) ) ) ).

thf(tp_c_2Eiterate_2EITSET,type,
    c_2Eiterate_2EITSET: del > del > $i ).

thf(mem_c_2Eiterate_2EITSET,axiom,
    ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eiterate_2EITSET @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27a @ A_27a ) ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ A_27a @ A_27a ) ) ) ) ).

thf(tp_c_2Eiterate_2ESum,type,
    c_2Eiterate_2ESum: del > $i ).

thf(mem_c_2Eiterate_2ESum,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eiterate_2ESum @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) @ ty_2Erealax_2Ereal ) ) ) ).

thf(tp_c_2Eiterate_2Einf,type,
    c_2Eiterate_2Einf: $i ).

thf(mem_c_2Eiterate_2Einf,axiom,
    mem @ c_2Eiterate_2Einf @ ( arr @ ( arr @ ty_2Erealax_2Ereal @ bool ) @ ty_2Erealax_2Ereal ) ).

thf(tp_c_2Eiterate_2Eiterate,type,
    c_2Eiterate_2Eiterate: del > del > $i ).

thf(mem_c_2Eiterate_2Eiterate,axiom,
    ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ A_27b ) ) ) ) ).

thf(tp_c_2Eiterate_2Emonoidal,type,
    c_2Eiterate_2Emonoidal: del > $i ).

thf(mem_c_2Eiterate_2Emonoidal,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) @ bool ) ) ).

thf(tp_c_2Eiterate_2Eneutral,type,
    c_2Eiterate_2Eneutral: del > $i ).

thf(mem_c_2Eiterate_2Eneutral,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eiterate_2Eneutral @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) @ A_27a ) ) ).

thf(tp_c_2Eiterate_2Ensum,type,
    c_2Eiterate_2Ensum: del > $i ).

thf(mem_c_2Eiterate_2Ensum,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ) ) ).

thf(tp_c_2Eiterate_2Epolynomial__function,type,
    c_2Eiterate_2Epolynomial__function: $i ).

thf(mem_c_2Eiterate_2Epolynomial__function,axiom,
    mem @ c_2Eiterate_2Epolynomial__function @ ( arr @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ bool ) ).

thf(tp_c_2Eiterate_2Esupport,type,
    c_2Eiterate_2Esupport: del > del > $i ).

thf(mem_c_2Eiterate_2Esupport,axiom,
    ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__LT__BETWEEN,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) )
    <=> ? [V2x: tp__ty_2Erealax_2Ereal] :
          ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) )
          & ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESIMP__REAL__ARCH,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal] :
    ? [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).

thf(conj_thm_2Eiterate_2ELOWER__BOUND__FINITE__SET__REAL,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
           => ? [V2a: tp__ty_2Erealax_2Ereal] :
              ! [V3x: $i] :
                ( ( mem @ V3x @ A_27a )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) @ ( ap @ V0f @ V3x ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EUPPER__BOUND__FINITE__SET__REAL,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
           => ? [V2a: tp__ty_2Erealax_2Ereal] :
              ! [V3x: $i] :
                ( ( mem @ V3x @ A_27a )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ V0f @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__WLOG__LT,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Erealax_2Ereal @ ( arr @ ty_2Erealax_2Ereal @ bool ) ) )
     => ( ( ! [V1x: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) )
          & ! [V2x: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal] :
              ( ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) )
            <=> ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) )
          & ! [V4x: tp__ty_2Erealax_2Ereal,V5y: tp__ty_2Erealax_2Ereal] :
              ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ ( inj__ty_2Erealax_2Ereal @ V5y ) ) )
             => ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ ( inj__ty_2Erealax_2Ereal @ V5y ) ) ) ) )
       => ! [V6x: tp__ty_2Erealax_2Ereal,V7y: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V6x ) ) @ ( inj__ty_2Erealax_2Ereal @ V7y ) ) ) ) ) ).

thf(ax_thm_2Eiterate_2EFINREC__def,axiom,
    ! [A_27a: del,A_27b: del] :
      ( ! [V0f: $i] :
          ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
         => ! [V1b: $i] :
              ( ( mem @ V1b @ A_27b )
             => ! [V2s: $i] :
                  ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
                 => ! [V3a: $i] :
                      ( ( mem @ V3a @ A_27b )
                     => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V0f ) @ V1b ) @ V2s ) @ V3a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
                      <=> ( ( V2s
                            = ( c_2Epred__set_2EEMPTY @ A_27a ) )
                          & ( V3a = V1b ) ) ) ) ) ) )
      & ! [V4f: $i] :
          ( ( mem @ V4f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
         => ! [V5b: $i] :
              ( ( mem @ V5b @ A_27b )
             => ! [V6s: $i] :
                  ( ( mem @ V6s @ ( arr @ A_27a @ bool ) )
                 => ! [V7a: $i] :
                      ( ( mem @ V7a @ A_27b )
                     => ! [V8n: tp__ty_2Enum_2Enum] :
                          ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V4f ) @ V5b ) @ V6s ) @ V7a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V8n ) ) ) )
                        <=> ? [V9x: $i] :
                              ( ( mem @ V9x @ A_27a )
                              & ? [V10c: $i] :
                                  ( ( mem @ V10c @ A_27b )
                                  & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V9x ) @ V6s ) )
                                  & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V4f ) @ V5b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V6s ) @ V9x ) ) @ V10c ) @ ( inj__ty_2Enum_2Enum @ V8n ) ) )
                                  & ( V7a
                                    = ( ap @ ( ap @ V4f @ V9x ) @ V10c ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINREC__def__compute,axiom,
    ! [A_27a: del,A_27b: del] :
      ( ! [V0f: $i] :
          ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
         => ! [V1b: $i] :
              ( ( mem @ V1b @ A_27b )
             => ! [V2s: $i] :
                  ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
                 => ! [V3a: $i] :
                      ( ( mem @ V3a @ A_27b )
                     => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V0f ) @ V1b ) @ V2s ) @ V3a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
                      <=> ( ( V2s
                            = ( c_2Epred__set_2EEMPTY @ A_27a ) )
                          & ( V3a = V1b ) ) ) ) ) ) )
      & ! [V4f: $i] :
          ( ( mem @ V4f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
         => ! [V5b: $i] :
              ( ( mem @ V5b @ A_27b )
             => ! [V6s: $i] :
                  ( ( mem @ V6s @ ( arr @ A_27a @ bool ) )
                 => ! [V7a: $i] :
                      ( ( mem @ V7a @ A_27b )
                     => ! [V8n: tp__ty_2Enum_2Enum] :
                          ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V4f ) @ V5b ) @ V6s ) @ V7a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8n ) ) ) ) )
                        <=> ? [V9x: $i] :
                              ( ( mem @ V9x @ A_27a )
                              & ? [V10c: $i] :
                                  ( ( mem @ V10c @ A_27b )
                                  & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V9x ) @ V6s ) )
                                  & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V4f ) @ V5b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V6s ) @ V9x ) ) @ V10c ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
                                  & ( V7a
                                    = ( ap @ ( ap @ V4f @ V9x ) @ V10c ) ) ) ) ) ) ) ) )
      & ! [V11f: $i] :
          ( ( mem @ V11f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
         => ! [V12b: $i] :
              ( ( mem @ V12b @ A_27b )
             => ! [V13s: $i] :
                  ( ( mem @ V13s @ ( arr @ A_27a @ bool ) )
                 => ! [V14a: $i] :
                      ( ( mem @ V14a @ A_27b )
                     => ! [V15n: tp__ty_2Enum_2Enum] :
                          ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V11f ) @ V12b ) @ V13s ) @ V14a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V15n ) ) ) ) )
                        <=> ? [V16x: $i] :
                              ( ( mem @ V16x @ A_27a )
                              & ? [V17c: $i] :
                                  ( ( mem @ V17c @ A_27b )
                                  & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V16x ) @ V13s ) )
                                  & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V11f ) @ V12b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V13s ) @ V16x ) ) @ V17c ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V15n ) ) ) ) )
                                  & ( V14a
                                    = ( ap @ ( ap @ V11f @ V16x ) @ V17c ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINREC__1__LEMMA,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ A_27b )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ! [V3a: $i] :
                  ( ( mem @ V3a @ A_27b )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V0f ) @ V1b ) @ V2s ) @ V3a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
                  <=> ? [V4x: $i] :
                        ( ( mem @ V4x @ A_27a )
                        & ( V2s
                          = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V4x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
                        & ( V3a
                          = ( ap @ ( ap @ V0f @ V4x ) @ V1b ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINREC__SUC__LEMMA,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ A_27b )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27a )
                   => ! [V4s: $i] :
                        ( ( mem @ V4s @ A_27b )
                       => ( ( V2x != V3y )
                         => ( ( ap @ ( ap @ V0f @ V2x ) @ ( ap @ ( ap @ V0f @ V3y ) @ V4s ) )
                            = ( ap @ ( ap @ V0f @ V3y ) @ ( ap @ ( ap @ V0f @ V2x ) @ V4s ) ) ) ) ) ) )
           => ! [V5n: tp__ty_2Enum_2Enum,V6s: $i] :
                ( ( mem @ V6s @ ( arr @ A_27a @ bool ) )
               => ! [V7z: $i] :
                    ( ( mem @ V7z @ A_27b )
                   => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V0f ) @ V1b ) @ V6s ) @ V7z ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) )
                     => ! [V8x: $i] :
                          ( ( mem @ V8x @ A_27a )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V8x ) @ V6s ) )
                           => ? [V9w: $i] :
                                ( ( mem @ V9w @ A_27b )
                                & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V0f ) @ V1b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V6s ) @ V8x ) ) @ V9w ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) )
                                & ( V7z
                                  = ( ap @ ( ap @ V0f @ V8x ) @ V9w ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINREC__UNIQUE__LEMMA,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ A_27b )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27a )
                   => ! [V4s: $i] :
                        ( ( mem @ V4s @ A_27b )
                       => ( ( V2x != V3y )
                         => ( ( ap @ ( ap @ V0f @ V2x ) @ ( ap @ ( ap @ V0f @ V3y ) @ V4s ) )
                            = ( ap @ ( ap @ V0f @ V3y ) @ ( ap @ ( ap @ V0f @ V2x ) @ V4s ) ) ) ) ) ) )
           => ! [V5n1: tp__ty_2Enum_2Enum,V6n2: tp__ty_2Enum_2Enum,V7s: $i] :
                ( ( mem @ V7s @ ( arr @ A_27a @ bool ) )
               => ! [V8a1: $i] :
                    ( ( mem @ V8a1 @ A_27b )
                   => ! [V9a2: $i] :
                        ( ( mem @ V9a2 @ A_27b )
                       => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V0f ) @ V1b ) @ V7s ) @ V8a1 ) @ ( inj__ty_2Enum_2Enum @ V5n1 ) ) )
                            & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V0f ) @ V1b ) @ V7s ) @ V9a2 ) @ ( inj__ty_2Enum_2Enum @ V6n2 ) ) ) )
                         => ( ( V8a1 = V9a2 )
                            & ( V5n1 = V6n2 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINREC__EXISTS__LEMMA,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ A_27b )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
               => ? [V3a: $i] :
                    ( ( mem @ V3a @ A_27b )
                    & ? [V4n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EFINREC @ A_27a @ A_27b ) @ V0f ) @ V1b ) @ V2s ) @ V3a ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINREC__FUN__LEMMA,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
     => ! [V1R: $i] :
          ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27b @ ( arr @ A_27c @ bool ) ) ) )
         => ( ( ! [V2s: $i] :
                  ( ( mem @ V2s @ A_27a )
                 => ( ( p @ ( ap @ V0P @ V2s ) )
                   => ? [V3a: $i] :
                        ( ( mem @ V3a @ A_27b )
                        & ? [V4n: $i] :
                            ( ( mem @ V4n @ A_27c )
                            & ( p @ ( ap @ ( ap @ ( ap @ V1R @ V2s ) @ V3a ) @ V4n ) ) ) ) ) )
              & ! [V5n1: $i] :
                  ( ( mem @ V5n1 @ A_27c )
                 => ! [V6n2: $i] :
                      ( ( mem @ V6n2 @ A_27c )
                     => ! [V7s: $i] :
                          ( ( mem @ V7s @ A_27a )
                         => ! [V8a1: $i] :
                              ( ( mem @ V8a1 @ A_27b )
                             => ! [V9a2: $i] :
                                  ( ( mem @ V9a2 @ A_27b )
                                 => ( ( ( p @ ( ap @ ( ap @ ( ap @ V1R @ V7s ) @ V8a1 ) @ V5n1 ) )
                                      & ( p @ ( ap @ ( ap @ ( ap @ V1R @ V7s ) @ V9a2 ) @ V6n2 ) ) )
                                   => ( ( V8a1 = V9a2 )
                                      & ( V5n1 = V6n2 ) ) ) ) ) ) ) ) )
           => ? [V10f: $i] :
                ( ( mem @ V10f @ ( arr @ A_27a @ A_27b ) )
                & ! [V11s: $i] :
                    ( ( mem @ V11s @ A_27a )
                   => ! [V12a: $i] :
                        ( ( mem @ V12a @ A_27b )
                       => ( ( p @ ( ap @ V0P @ V11s ) )
                         => ( ? [V13n: $i] :
                                ( ( mem @ V13n @ A_27c )
                                & ( p @ ( ap @ ( ap @ ( ap @ V1R @ V11s ) @ V12a ) @ V13n ) ) )
                          <=> ( ( ap @ V10f @ V11s )
                              = V12a ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINREC__FUN,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ A_27b )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27a )
                   => ! [V4s: $i] :
                        ( ( mem @ V4s @ A_27b )
                       => ( ( V2x != V3y )
                         => ( ( ap @ ( ap @ V0f @ V2x ) @ ( ap @ ( ap @ V0f @ V3y ) @ V4s ) )
                            = ( ap @ ( ap @ V0f @ V3y ) @ ( ap @ ( ap @ V0f @ V2x ) @ V4s ) ) ) ) ) ) )
           => ? [V5g: $i] :
                ( ( mem @ V5g @ ( arr @ ( arr @ A_27a @ bool ) @ A_27b ) )
                & ( ( ap @ V5g @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
                  = V1b )
                & ! [V6s: $i] :
                    ( ( mem @ V6s @ ( arr @ A_27a @ bool ) )
                   => ! [V7x: $i] :
                        ( ( mem @ V7x @ A_27a )
                       => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V6s ) )
                            & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7x ) @ V6s ) ) )
                         => ( ( ap @ V5g @ V6s )
                            = ( ap @ ( ap @ V0f @ V7x ) @ ( ap @ V5g @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V6s ) @ V7x ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESET__RECURSION__LEMMA,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ A_27b )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27a )
                   => ! [V4s: $i] :
                        ( ( mem @ V4s @ A_27b )
                       => ( ( V2x != V3y )
                         => ( ( ap @ ( ap @ V0f @ V2x ) @ ( ap @ ( ap @ V0f @ V3y ) @ V4s ) )
                            = ( ap @ ( ap @ V0f @ V3y ) @ ( ap @ ( ap @ V0f @ V2x ) @ V4s ) ) ) ) ) ) )
           => ? [V5g: $i] :
                ( ( mem @ V5g @ ( arr @ ( arr @ A_27a @ bool ) @ A_27b ) )
                & ( ( ap @ V5g @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
                  = V1b )
                & ! [V6x: $i] :
                    ( ( mem @ V6x @ A_27a )
                   => ! [V7s: $i] :
                        ( ( mem @ V7s @ ( arr @ A_27a @ bool ) )
                       => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V7s ) )
                         => ( ( ap @ V5g @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V6x ) @ V7s ) )
                            = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V7s ) ) @ ( ap @ V5g @ V7s ) ) @ ( ap @ ( ap @ V0f @ V6x ) @ ( ap @ V5g @ V7s ) ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eiterate_2EITSET__def,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27a @ A_27a ) ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
         => ! [V2b: $i] :
              ( ( mem @ V2b @ A_27a )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EITSET @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2b )
                = ( ap
                  @ ( ap @ ( c_2Emin_2E_40 @ ( arr @ ( arr @ A_27b @ bool ) @ A_27a ) )
                    @ ( lam @ ( arr @ ( arr @ A_27b @ bool ) @ A_27a )
                      @ ^ [V3g: $i] :
                          ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V3g @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) @ V2b ) )
                          @ ( ap @ ( c_2Ebool_2E_21 @ A_27b )
                            @ ( lam @ A_27b
                              @ ^ [V4x: $i] :
                                  ( ap @ ( c_2Ebool_2E_21 @ ( arr @ A_27b @ bool ) )
                                  @ ( lam @ ( arr @ A_27b @ bool )
                                    @ ^ [V5s: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V5s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V3g @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V4x ) @ V5s ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4x ) @ V5s ) ) @ ( ap @ V3g @ V5s ) ) @ ( ap @ ( ap @ V0f @ V4x ) @ ( ap @ V3g @ V5s ) ) ) ) ) ) ) ) ) ) ) )
                  @ V1s ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINITE__RECURSION,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ A_27b )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ! [V3y: $i] :
                    ( ( mem @ V3y @ A_27a )
                   => ! [V4s: $i] :
                        ( ( mem @ V4s @ A_27b )
                       => ( ( V2x != V3y )
                         => ( ( ap @ ( ap @ V0f @ V2x ) @ ( ap @ ( ap @ V0f @ V3y ) @ V4s ) )
                            = ( ap @ ( ap @ V0f @ V3y ) @ ( ap @ ( ap @ V0f @ V2x ) @ V4s ) ) ) ) ) ) )
           => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EITSET @ A_27b @ A_27a ) @ V0f ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V1b )
                = V1b )
              & ! [V5x: $i] :
                  ( ( mem @ V5x @ A_27a )
                 => ! [V6s: $i] :
                      ( ( mem @ V6s @ ( arr @ A_27a @ bool ) )
                     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V6s ) )
                       => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EITSET @ A_27b @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V5x ) @ V6s ) ) @ V1b )
                          = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V6s ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EITSET @ A_27b @ A_27a ) @ V0f ) @ V6s ) @ V1b ) ) @ ( ap @ ( ap @ V0f @ V5x ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2EITSET @ A_27b @ A_27a ) @ V0f ) @ V6s ) @ V1b ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ECARD__UNION__EQ,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
         => ! [V2u: $i] :
              ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2u ) )
                  & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t )
                    = ( c_2Epred__set_2EEMPTY @ A_27a ) )
                  & ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t )
                    = V2u ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1t ) ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V2u ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUBSET__RESTRICT,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1P: $i] :
          ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
         => ( p
            @ ( ap
              @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a )
                @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                  @ ( lam @ A_27a
                    @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) ) @ ( ap @ V1P @ V2x ) ) ) ) ) )
              @ V0s ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINITE__RESTRICT,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1P: $i] :
          ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
           => ( p
              @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
                @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                  @ ( lam @ A_27a
                    @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) ) @ ( ap @ V1P @ V2x ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINITE__REAL__INTERVAL,axiom,
    ( ! [V0a: tp__ty_2Erealax_2Ereal] :
        ~ ( p
          @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V1x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V1x ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) @ V1x ) ) ) ) ) )
    & ! [V2a: tp__ty_2Erealax_2Ereal] :
        ~ ( p
          @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V3x ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) @ V3x ) ) ) ) ) )
    & ! [V4b: tp__ty_2Erealax_2Ereal] :
        ~ ( p
          @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V5x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V5x ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ V5x ) @ ( inj__ty_2Erealax_2Ereal @ V4b ) ) ) ) ) ) )
    & ! [V6b: tp__ty_2Erealax_2Ereal] :
        ~ ( p
          @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V7x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V7x ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ V7x ) @ ( inj__ty_2Erealax_2Ereal @ V6b ) ) ) ) ) ) )
    & ! [V8a: tp__ty_2Erealax_2Ereal,V9b: tp__ty_2Erealax_2Ereal] :
        ( ( p
          @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V10x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V10x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V8a ) ) @ V10x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ V10x ) @ ( inj__ty_2Erealax_2Ereal @ V9b ) ) ) ) ) ) ) )
      <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V9b ) ) @ ( inj__ty_2Erealax_2Ereal @ V8a ) ) ) )
    & ! [V11a: tp__ty_2Erealax_2Ereal,V12b: tp__ty_2Erealax_2Ereal] :
        ( ( p
          @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V13x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V13x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V11a ) ) @ V13x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ V13x ) @ ( inj__ty_2Erealax_2Ereal @ V12b ) ) ) ) ) ) ) )
      <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V12b ) ) @ ( inj__ty_2Erealax_2Ereal @ V11a ) ) ) )
    & ! [V14a: tp__ty_2Erealax_2Ereal,V15b: tp__ty_2Erealax_2Ereal] :
        ( ( p
          @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V16x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V16x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V14a ) ) @ V16x ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ V16x ) @ ( inj__ty_2Erealax_2Ereal @ V15b ) ) ) ) ) ) ) )
      <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V15b ) ) @ ( inj__ty_2Erealax_2Ereal @ V14a ) ) ) )
    & ! [V17a: tp__ty_2Erealax_2Ereal,V18b: tp__ty_2Erealax_2Ereal] :
        ( ( p
          @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V19x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V19x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V17a ) ) @ V19x ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ V19x ) @ ( inj__ty_2Erealax_2Ereal @ V18b ) ) ) ) ) ) ) )
      <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V18b ) ) @ ( inj__ty_2Erealax_2Ereal @ V17a ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2Ereal__INFINITE,axiom,
    ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ ( c_2Epred__set_2EUNIV @ ty_2Erealax_2Ereal ) ) ) ).

thf(conj_thm_2Eiterate_2ESET__PROVE__CASES,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
     => ( ( ( p @ ( ap @ V0P @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
          & ! [V1a: $i] :
              ( ( mem @ V1a @ A_27a )
             => ! [V2s: $i] :
                  ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
                 => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1a ) @ V2s ) )
                   => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1a ) @ V2s ) ) ) ) ) ) )
       => ! [V3s: $i] :
            ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
           => ( p @ ( ap @ V0P @ V3s ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ECHOOSE__SUBSET__STRONG,axiom,
    ! [A_27a: del,V0n: tp__ty_2Enum_2Enum,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 @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) ) )
       => ? [V2t: $i] :
            ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
            & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2t ) @ V1s ) )
            & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V2t ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ECHOOSE__SUBSET,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
       => ! [V1n: tp__ty_2Enum_2Enum] :
            ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) )
           => ? [V2t: $i] :
                ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
                & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2t ) @ V0s ) )
                & ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V2t ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__COMPLETE,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( ? [V1x: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) )
          & ? [V2M: tp__ty_2Erealax_2Ereal] :
            ! [V3x: tp__ty_2Erealax_2Ereal] :
              ( ( p @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2M ) ) ) ) )
       => ? [V4M: tp__ty_2Erealax_2Ereal] :
            ( ! [V5x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) @ ( inj__ty_2Erealax_2Ereal @ V4M ) ) ) )
            & ! [V6M_27: tp__ty_2Erealax_2Ereal] :
                ( ! [V7x: tp__ty_2Erealax_2Ereal] :
                    ( ( p @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V7x ) ) )
                   => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V7x ) ) @ ( inj__ty_2Erealax_2Ereal @ V6M_27 ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V4M ) ) @ ( inj__ty_2Erealax_2Ereal @ V6M_27 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2Esup__alt,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Esup @ V0s ) )
        = ( surj__ty_2Erealax_2Ereal
          @ ( ap @ ( c_2Emin_2E_40 @ ty_2Erealax_2Ereal )
            @ ( lam @ ty_2Erealax_2Ereal
              @ ^ [V1a: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_2F_5C
                    @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Erealax_2Ereal )
                      @ ( lam @ ty_2Erealax_2Ereal
                        @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ V2x ) @ V0s ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ V2x ) @ V1a ) ) ) ) )
                  @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Erealax_2Ereal )
                    @ ( lam @ ty_2Erealax_2Ereal
                      @ ^ [V3b: $i] :
                          ( ap
                          @ ( ap @ c_2Emin_2E_3D_3D_3E
                            @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Erealax_2Ereal )
                              @ ( lam @ ty_2Erealax_2Ereal
                                @ ^ [V4x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ V4x ) @ V0s ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ V4x ) @ V3b ) ) ) ) )
                          @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ V1a ) @ V3b ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUP__EQ,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
         => ( ! [V2b: tp__ty_2Erealax_2Ereal] :
                ( ! [V3x: tp__ty_2Erealax_2Ereal] :
                    ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
                   => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) )
              <=> ! [V4x: tp__ty_2Erealax_2Ereal] :
                    ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ V1t ) )
                   => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) )
           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Esup @ V0s ) )
              = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Esup @ V1t ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUP,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( ( V0s
           != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
          & ? [V1b: tp__ty_2Erealax_2Ereal] :
            ! [V2x: tp__ty_2Erealax_2Ereal] :
              ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) ) ) )
       => ( ! [V3x: tp__ty_2Erealax_2Ereal] :
              ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( ap @ c_2Ereal_2Esup @ V0s ) ) ) )
          & ! [V4b: tp__ty_2Erealax_2Ereal] :
              ( ! [V5x: tp__ty_2Erealax_2Ereal] :
                  ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) @ V0s ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) @ ( inj__ty_2Erealax_2Ereal @ V4b ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Esup @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V4b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUP__FINITE__LEMMA,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
          & ( V0s
           != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
       => ? [V1b: tp__ty_2Erealax_2Ereal] :
            ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) @ V0s ) )
            & ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUP__FINITE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
          & ( V0s
           != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( ap @ c_2Ereal_2Esup @ V0s ) ) @ V0s ) )
          & ! [V1x: tp__ty_2Erealax_2Ereal] :
              ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ V0s ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( ap @ c_2Ereal_2Esup @ V0s ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__LE__SUP__FINITE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
            & ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( ap @ c_2Ereal_2Esup @ V0s ) ) )
          <=> ? [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
                & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUP__LE__FINITE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
            & ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Esup @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) )
          <=> ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__LT__SUP__FINITE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
            & ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( ap @ c_2Ereal_2Esup @ V0s ) ) )
          <=> ? [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
                & ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUP__LT__FINITE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
            & ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Esup @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) )
          <=> ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUP__LE__EQ,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1y: tp__ty_2Erealax_2Ereal] :
          ( ( ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
            & ? [V2b: tp__ty_2Erealax_2Ereal] :
              ! [V3x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Esup @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
          <=> ! [V4x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUP__UNIQUE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1b: tp__ty_2Erealax_2Ereal] :
          ( ( ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) ) )
            & ! [V3b_27: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V3b_27 ) ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) )
               => ? [V4x: tp__ty_2Erealax_2Ereal] :
                    ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ V0s ) )
                    & ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V3b_27 ) ) @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) ) ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Esup @ V0s ) )
            = V1b ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUP__LE__S,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1b: tp__ty_2Erealax_2Ereal] :
          ( ( ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
            & ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) ) ) )
         => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Esup @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUP__LE__SUBSET,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
         => ( ( ( V0s
               != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
              & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Erealax_2Ereal ) @ V0s ) @ V1t ) )
              & ? [V2b: tp__ty_2Erealax_2Ereal] :
                ! [V3x: tp__ty_2Erealax_2Ereal] :
                  ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V1t ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) )
           => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Esup @ V0s ) ) @ ( ap @ c_2Ereal_2Esup @ V1t ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__LE__SUP,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal] :
          ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) @ V0s ) )
            & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) )
            & ! [V4x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) )
         => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( ap @ c_2Ereal_2Esup @ V0s ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUP__BOUNDS,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
          ( ( ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
            & ! [V3x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
               => ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) )
                  & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( ap @ c_2Ereal_2Esup @ V0s ) ) )
            & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Esup @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__ABS__SUP__LE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
            & ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) ) ) )
         => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ c_2Ereal_2Esup @ V0s ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUP__ASCLOSE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1l: tp__ty_2Erealax_2Ereal,V2e: tp__ty_2Erealax_2Ereal] :
          ( ( ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
            & ! [V3x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1l ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) ) )
         => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Ereal_2Esup @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V1l ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUP__SING,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Esup @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) ) )
      = V0a ) ).

thf(conj_thm_2Eiterate_2ESUP__UNIQUE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1b: tp__ty_2Erealax_2Ereal] :
          ( ! [V2c: tp__ty_2Erealax_2Ereal] :
              ( ! [V3x: tp__ty_2Erealax_2Ereal] :
                  ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2c ) ) ) )
            <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) @ ( inj__ty_2Erealax_2Ereal @ V2c ) ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Esup @ V0s ) )
            = V1b ) ) ) ).

thf(conj_thm_2Eiterate_2ESUP__UNION,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
         => ( ( ( V0s
               != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
              & ( V1t
               != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
              & ? [V2b: tp__ty_2Erealax_2Ereal] :
                ! [V3x: tp__ty_2Erealax_2Ereal] :
                  ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) )
              & ? [V4c: tp__ty_2Erealax_2Ereal] :
                ! [V5x: tp__ty_2Erealax_2Ereal] :
                  ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) @ V1t ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) @ ( inj__ty_2Erealax_2Ereal @ V4c ) ) ) ) )
           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Esup @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Erealax_2Ereal ) @ V0s ) @ V1t ) ) )
              = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Emax @ ( ap @ c_2Ereal_2Esup @ V0s ) ) @ ( ap @ c_2Ereal_2Esup @ V1t ) ) ) ) ) ) ) ).

thf(ax_thm_2Eiterate_2Einf,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eiterate_2Einf @ V0s ) )
        = ( surj__ty_2Erealax_2Ereal
          @ ( ap @ ( c_2Emin_2E_40 @ ty_2Erealax_2Ereal )
            @ ( lam @ ty_2Erealax_2Ereal
              @ ^ [V1a: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_2F_5C
                    @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Erealax_2Ereal )
                      @ ( lam @ ty_2Erealax_2Ereal
                        @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ V2x ) @ V0s ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ V1a ) @ V2x ) ) ) ) )
                  @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Erealax_2Ereal )
                    @ ( lam @ ty_2Erealax_2Ereal
                      @ ^ [V3b: $i] :
                          ( ap
                          @ ( ap @ c_2Emin_2E_3D_3D_3E
                            @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Erealax_2Ereal )
                              @ ( lam @ ty_2Erealax_2Ereal
                                @ ^ [V4x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ V4x ) @ V0s ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ V3b ) @ V4x ) ) ) ) )
                          @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ V3b ) @ V1a ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EINF__EQ,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
         => ( ! [V2a: tp__ty_2Erealax_2Ereal] :
                ( ! [V3x: tp__ty_2Erealax_2Ereal] :
                    ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
                   => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) ) )
              <=> ! [V4x: tp__ty_2Erealax_2Ereal] :
                    ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ V1t ) )
                   => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) ) ) )
           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eiterate_2Einf @ V0s ) )
              = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eiterate_2Einf @ V1t ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EINF,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( ( V0s
           != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
          & ? [V1b: tp__ty_2Erealax_2Ereal] :
            ! [V2x: tp__ty_2Erealax_2Ereal] :
              ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) ) )
       => ( ! [V3x: tp__ty_2Erealax_2Ereal] :
              ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) ) )
          & ! [V4b: tp__ty_2Erealax_2Ereal] :
              ( ! [V5x: tp__ty_2Erealax_2Ereal] :
                  ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) @ V0s ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V4b ) ) @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V4b ) ) @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EINF__FINITE__LEMMA,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
          & ( V0s
           != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
       => ? [V1b: tp__ty_2Erealax_2Ereal] :
            ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) @ V0s ) )
            & ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EINF__FINITE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
          & ( V0s
           != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) @ V0s ) )
          & ! [V1x: tp__ty_2Erealax_2Ereal] :
              ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ V0s ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__LE__INF__FINITE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
            & ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) )
          <=> ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__INF__LE__FINITE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
            & ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) )
          <=> ? [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
                & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__LT__INF__FINITE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
            & ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) )
          <=> ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__INF__LT__FINITE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V0s ) )
            & ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) )
          <=> ? [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
                & ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__INF__UNIQUE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1b: tp__ty_2Erealax_2Ereal] :
          ( ( ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) )
            & ! [V3b_27: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) @ ( inj__ty_2Erealax_2Ereal @ V3b_27 ) ) )
               => ? [V4x: tp__ty_2Erealax_2Ereal] :
                    ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ V0s ) )
                    & ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V4x ) ) @ ( inj__ty_2Erealax_2Ereal @ V3b_27 ) ) ) ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eiterate_2Einf @ V0s ) )
            = V1b ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__LE__INF,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1b: tp__ty_2Erealax_2Ereal] :
          ( ( ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
            & ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) ) )
         => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__LE__INF__SUBSET,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
         => ( ( ( V1t
               != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
              & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Erealax_2Ereal ) @ V1t ) @ V0s ) )
              & ? [V2b: tp__ty_2Erealax_2Ereal] :
                ! [V3x: tp__ty_2Erealax_2Ereal] :
                  ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) ) ) )
           => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) @ ( ap @ c_2Eiterate_2Einf @ V1t ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__INF__BOUNDS,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal,V2b: tp__ty_2Erealax_2Ereal] :
          ( ( ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
            & ! [V3x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
               => ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) )
                  & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) )
         => ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) )
            & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__ABS__INF__LE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
            & ! [V2x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) ) ) )
         => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__INF__ASCLOSE,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1l: tp__ty_2Erealax_2Ereal,V2e: tp__ty_2Erealax_2Ereal] :
          ( ( ( V0s
             != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
            & ! [V3x: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V0s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1l ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) ) )
         => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) @ ( inj__ty_2Erealax_2Ereal @ V1l ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUP__UNIQUE__FINITE,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1s: $i] :
      ( ( mem @ V1s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V1s ) )
          & ( V1s
           != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
       => ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Esup @ V1s ) )
            = V0a )
        <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) @ V1s ) )
            & ! [V2y: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ V1s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EINF__UNIQUE__FINITE,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1s: $i] :
      ( ( mem @ V1s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V1s ) )
          & ( V1s
           != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) )
       => ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eiterate_2Einf @ V1s ) )
            = V0a )
        <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) @ V1s ) )
            & ! [V2y: tp__ty_2Erealax_2Ereal] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ V1s ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUP__INSERT__FINITE,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1s: $i] :
      ( ( mem @ V1s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V1s ) )
       => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Esup @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ V1s ) ) )
          = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ ty_2Erealax_2Ereal @ bool ) ) @ V1s ) @ ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Ereal_2Emax @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ c_2Ereal_2Esup @ V1s ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EINF__INSERT__FINITE,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1s: $i] :
      ( ( mem @ V1s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal ) @ V1s ) )
       => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eiterate_2Einf @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ V1s ) ) )
          = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ ty_2Erealax_2Ereal @ bool ) ) @ V1s ) @ ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Ereal_2Emin @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ c_2Eiterate_2Einf @ V1s ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUP__EQ__INF,axiom,
    ! [V0s: $i] :
      ( ( mem @ V0s @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ( ( ( V0s
           != ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) )
          & ? [V1B: tp__ty_2Erealax_2Ereal] :
            ! [V2x: tp__ty_2Erealax_2Ereal] :
              ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V0s ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1B ) ) ) ) )
       => ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Esup @ V0s ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eiterate_2Einf @ V0s ) ) )
        <=> ? [V3a: tp__ty_2Erealax_2Ereal] :
              ( V0s
              = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V3a ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EINF__SING,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eiterate_2Einf @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Erealax_2Ereal ) ) ) )
      = V0a ) ).

thf(ax_thm_2Eiterate_2Enumseg,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
      = ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
        @ ( lam @ ty_2Enum_2Enum
          @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ bool ) @ V2x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V2x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V2x ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINITE__NUMSEG,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__COMBINE__R,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1p: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
      ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
        & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
     => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1p ) ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
        = ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__COMBINE__L,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1p: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
      ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1p ) ) )
        & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
     => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
        = ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__LREC,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 ) ) )
     => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
        = ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__RREC,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 ) ) )
     => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
        = ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__REC,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
     => ( ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
        = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EIN__NUMSEG,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( 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 @ V2p ) ) )
        & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EIN__NUMSEG__0,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( 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_2Eiterate_2ENUMSEG__SING,axiom,
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
      = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__EMPTY,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
        = ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
    <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).

thf(conj_thm_2Eiterate_2ECARD__NUMSEG__LEMMA,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1d: tp__ty_2Enum_2Enum] :
      ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1d ) ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1d ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ECARD__NUMSEG,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).

thf(conj_thm_2Eiterate_2EHAS__SIZE__NUMSEG,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).

thf(conj_thm_2Eiterate_2ECARD__NUMSEG__1,axiom,
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
      = V0n ) ).

thf(conj_thm_2Eiterate_2EHAS__SIZE__NUMSEG__1,axiom,
    ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__CLAUSES,axiom,
    ( ! [V0m: tp__ty_2Enum_2Enum] :
        ( ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) )
    & ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
        ( ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINITE__INDEX__NUMSEG,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
      <=> ? [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
            & ! [V2i: tp__ty_2Enum_2Enum,V3j: tp__ty_2Enum_2Enum] :
                ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3j ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) )
                  & ( ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V2i ) )
                    = ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V3j ) ) ) )
               => ( V2i = V3j ) )
            & ( V0s
              = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ A_27a ) @ V1f ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINITE__INDEX__NUMBERS,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
      <=> ? [V1k: $i] :
            ( ( mem @ V1k @ ( arr @ ty_2Enum_2Enum @ bool ) )
            & ? [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
                & ! [V3i: tp__ty_2Enum_2Enum,V4j: tp__ty_2Enum_2Enum] :
                    ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ V1k ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V4j ) ) @ V1k ) )
                      & ( ( ap @ V2f @ ( inj__ty_2Enum_2Enum @ V3i ) )
                        = ( ap @ V2f @ ( inj__ty_2Enum_2Enum @ V4j ) ) ) )
                   => ( V3i = V4j ) )
                & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V1k ) )
                & ( V0s
                  = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ A_27a ) @ V2f ) @ V1k ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EDISJOINT__NUMSEG,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum,V3q: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V3q ) ) ) )
    <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
        | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3q ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
        | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
        | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3q ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__ADD__SPLIT,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
     => ( ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
        = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__OFFSET__IMAGE,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
      ( ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
      = ( ap
        @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
          @ ( lam @ ty_2Enum_2Enum
            @ ^ [V3i: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3i ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
        @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUBSET__NUMSEG,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum,V3q: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V3q ) ) ) )
    <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
        | ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
          & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V3q ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__LE,axiom,
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
        @ ( lam @ ty_2Enum_2Enum
          @ ^ [V1x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ bool ) @ V1x ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V1x ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
      = ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).

thf(conj_thm_2Eiterate_2ENUMSEG__LT,axiom,
    ! [V0n: tp__ty_2Enum_2Enum] :
      ( ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
        @ ( lam @ ty_2Enum_2Enum
          @ ^ [V1x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ bool ) @ V1x ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V1x ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
      = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ETOPOLOGICAL__SORT,axiom,
    ! [A_27a: del,V0_3C_3C: $i] :
      ( ( mem @ V0_3C_3C @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
     => ( ( ! [V1x: $i] :
              ( ( mem @ V1x @ A_27a )
             => ! [V2y: $i] :
                  ( ( mem @ V2y @ A_27a )
                 => ( ( ( p @ ( ap @ ( ap @ V0_3C_3C @ V1x ) @ V2y ) )
                      & ( p @ ( ap @ ( ap @ V0_3C_3C @ V2y ) @ V1x ) ) )
                   => ( V1x = V2y ) ) ) )
          & ! [V3x: $i] :
              ( ( mem @ V3x @ A_27a )
             => ! [V4y: $i] :
                  ( ( mem @ V4y @ A_27a )
                 => ! [V5z: $i] :
                      ( ( mem @ V5z @ A_27a )
                     => ( ( ( p @ ( ap @ ( ap @ V0_3C_3C @ V3x ) @ V4y ) )
                          & ( p @ ( ap @ ( ap @ V0_3C_3C @ V4y ) @ V5z ) ) )
                       => ( p @ ( ap @ ( ap @ V0_3C_3C @ V3x ) @ V5z ) ) ) ) ) ) )
       => ! [V6n: tp__ty_2Enum_2Enum,V7s: $i] :
            ( ( mem @ V7s @ ( arr @ A_27a @ bool ) )
           => ( ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2EHAS__SIZE @ A_27a ) @ V7s ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) )
             => ? [V8f: $i] :
                  ( ( mem @ V8f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
                  & ( V7s
                    = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ A_27a ) @ V8f ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) )
                  & ! [V9j: tp__ty_2Enum_2Enum,V10k: tp__ty_2Enum_2Enum] :
                      ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V9j ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V10k ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) )
                        & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V9j ) ) @ ( inj__ty_2Enum_2Enum @ V10k ) ) ) )
                     => ~ ( p @ ( ap @ ( ap @ V0_3C_3C @ ( ap @ V8f @ ( inj__ty_2Enum_2Enum @ V10k ) ) ) @ ( ap @ V8f @ ( inj__ty_2Enum_2Enum @ V9j ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eiterate_2Eneutral,axiom,
    ! [A_27a: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ( ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op )
        = ( ap @ ( c_2Emin_2E_40 @ A_27a )
          @ ( lam @ A_27a
            @ ^ [V1x: $i] :
                ( ap @ ( c_2Ebool_2E_21 @ A_27a )
                @ ( lam @ A_27a
                  @ ^ [V2y: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ ( ap @ V0op @ V1x ) @ V2y ) ) @ V2y ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ ( ap @ V0op @ V2y ) @ V1x ) ) @ V2y ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eiterate_2Emonoidal,axiom,
    ! [A_27a: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ V0op ) )
      <=> ( ! [V1x: $i] :
              ( ( mem @ V1x @ A_27a )
             => ! [V2y: $i] :
                  ( ( mem @ V2y @ A_27a )
                 => ( ( ap @ ( ap @ V0op @ V1x ) @ V2y )
                    = ( ap @ ( ap @ V0op @ V2y ) @ V1x ) ) ) )
          & ! [V3x: $i] :
              ( ( mem @ V3x @ A_27a )
             => ! [V4y: $i] :
                  ( ( mem @ V4y @ A_27a )
                 => ! [V5z: $i] :
                      ( ( mem @ V5z @ A_27a )
                     => ( ( ap @ ( ap @ V0op @ V3x ) @ ( ap @ ( ap @ V0op @ V4y ) @ V5z ) )
                        = ( ap @ ( ap @ V0op @ ( ap @ ( ap @ V0op @ V3x ) @ V4y ) ) @ V5z ) ) ) ) )
          & ! [V6x: $i] :
              ( ( mem @ V6x @ A_27a )
             => ( ( ap @ ( ap @ V0op @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op ) ) @ V6x )
                = V6x ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EMONOIDAL__AC,axiom,
    ! [A_27a: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ V0op ) )
       => ( ! [V1a: $i] :
              ( ( mem @ V1a @ A_27a )
             => ( ( ap @ ( ap @ V0op @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op ) ) @ V1a )
                = V1a ) )
          & ! [V2a: $i] :
              ( ( mem @ V2a @ A_27a )
             => ( ( ap @ ( ap @ V0op @ V2a ) @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op ) )
                = V2a ) )
          & ! [V3a: $i] :
              ( ( mem @ V3a @ A_27a )
             => ! [V4b: $i] :
                  ( ( mem @ V4b @ A_27a )
                 => ( ( ap @ ( ap @ V0op @ V3a ) @ V4b )
                    = ( ap @ ( ap @ V0op @ V4b ) @ V3a ) ) ) )
          & ! [V5a: $i] :
              ( ( mem @ V5a @ A_27a )
             => ! [V6b: $i] :
                  ( ( mem @ V6b @ A_27a )
                 => ! [V7c: $i] :
                      ( ( mem @ V7c @ A_27a )
                     => ( ( ap @ ( ap @ V0op @ ( ap @ ( ap @ V0op @ V5a ) @ V6b ) ) @ V7c )
                        = ( ap @ ( ap @ V0op @ V5a ) @ ( ap @ ( ap @ V0op @ V6b ) @ V7c ) ) ) ) ) )
          & ! [V8a: $i] :
              ( ( mem @ V8a @ A_27a )
             => ! [V9b: $i] :
                  ( ( mem @ V9b @ A_27a )
                 => ! [V10c: $i] :
                      ( ( mem @ V10c @ A_27a )
                     => ( ( ap @ ( ap @ V0op @ V8a ) @ ( ap @ ( ap @ V0op @ V9b ) @ V10c ) )
                        = ( ap @ ( ap @ V0op @ V9b ) @ ( ap @ ( ap @ V0op @ V8a ) @ V10c ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eiterate_2Esupport,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V1f ) @ V2s )
                = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                  @ ( lam @ A_27a
                    @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V1f @ V3x ) ) @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eiterate_2Eiterate,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V1s ) @ V2f )
                = ( ap
                  @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V2f ) @ V1s ) ) )
                    @ ( ap
                      @ ( ap
                        @ ( ap @ ( c_2Eiterate_2EITSET @ A_27b @ A_27a )
                          @ ( lam @ A_27a
                            @ ^ [V3x: $i] :
                                ( lam @ A_27b
                                @ ^ [V4a: $i] : ( ap @ ( ap @ V0op @ ( ap @ V2f @ V3x ) ) @ V4a ) ) ) )
                        @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V2f ) @ V1s ) )
                      @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) )
                  @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EIN__SUPPORT,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
         => ! [V2x: $i] :
              ( ( mem @ V2x @ A_27b )
             => ! [V3s: $i] :
                  ( ( mem @ V3s @ ( arr @ A_27b @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V2x ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V1f ) @ V3s ) ) )
                  <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V2x ) @ V3s ) )
                      & ( ( ap @ V1f @ V2x )
                       != ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUPPORT__SUPPORT,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V1f ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V1f ) @ V2s ) )
                = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V1f ) @ V2s ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUPPORT__EMPTY,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
             => ( ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27b )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3x ) @ V2s ) )
                     => ( ( ap @ V1f @ V3x )
                        = ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op ) ) ) )
              <=> ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V1f ) @ V2s )
                  = ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUPPORT__SUBSET,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
             => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V1f ) @ V2s ) ) @ V2s ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINITE__SUPPORT,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
             => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2s ) )
               => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V1f ) @ V2s ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUPPORT__CLAUSES,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,A_27f: del,A_27g: del,A_27h: del,A_27i: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V1f ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
              = ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
        & ! [V2f: $i] :
            ( ( mem @ V2f @ ( arr @ A_27c @ A_27b ) )
           => ! [V3x: $i] :
                ( ( mem @ V3x @ A_27c )
               => ! [V4s: $i] :
                    ( ( mem @ V4s @ ( arr @ A_27c @ bool ) )
                   => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27c @ A_27b ) @ V0op ) @ V2f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27c ) @ V3x ) @ V4s ) )
                      = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ A_27c @ bool ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V2f @ V3x ) ) @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27c @ A_27b ) @ V0op ) @ V2f ) @ V4s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27c ) @ V3x ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27c @ A_27b ) @ V0op ) @ V2f ) @ V4s ) ) ) ) ) ) )
        & ! [V5f: $i] :
            ( ( mem @ V5f @ ( arr @ A_27d @ A_27b ) )
           => ! [V6x: $i] :
                ( ( mem @ V6x @ A_27d )
               => ! [V7s: $i] :
                    ( ( mem @ V7s @ ( arr @ A_27d @ bool ) )
                   => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27d @ A_27b ) @ V0op ) @ V5f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27d ) @ V7s ) @ V6x ) )
                      = ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27d ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27d @ A_27b ) @ V0op ) @ V5f ) @ V7s ) ) @ V6x ) ) ) ) )
        & ! [V8f: $i] :
            ( ( mem @ V8f @ ( arr @ A_27e @ A_27b ) )
           => ! [V9s: $i] :
                ( ( mem @ V9s @ ( arr @ A_27e @ bool ) )
               => ! [V10t: $i] :
                    ( ( mem @ V10t @ ( arr @ A_27e @ bool ) )
                   => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27e @ A_27b ) @ V0op ) @ V8f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27e ) @ V9s ) @ V10t ) )
                      = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27e ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27e @ A_27b ) @ V0op ) @ V8f ) @ V9s ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27e @ A_27b ) @ V0op ) @ V8f ) @ V10t ) ) ) ) ) )
        & ! [V11f: $i] :
            ( ( mem @ V11f @ ( arr @ A_27f @ A_27b ) )
           => ! [V12s: $i] :
                ( ( mem @ V12s @ ( arr @ A_27f @ bool ) )
               => ! [V13t: $i] :
                    ( ( mem @ V13t @ ( arr @ A_27f @ bool ) )
                   => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27f @ A_27b ) @ V0op ) @ V11f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27f ) @ V12s ) @ V13t ) )
                      = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27f ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27f @ A_27b ) @ V0op ) @ V11f ) @ V12s ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27f @ A_27b ) @ V0op ) @ V11f ) @ V13t ) ) ) ) ) )
        & ! [V14f: $i] :
            ( ( mem @ V14f @ ( arr @ A_27g @ A_27b ) )
           => ! [V15s: $i] :
                ( ( mem @ V15s @ ( arr @ A_27g @ bool ) )
               => ! [V16t: $i] :
                    ( ( mem @ V16t @ ( arr @ A_27g @ bool ) )
                   => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27g @ A_27b ) @ V0op ) @ V14f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27g ) @ V15s ) @ V16t ) )
                      = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27g ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27g @ A_27b ) @ V0op ) @ V14f ) @ V15s ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27g @ A_27b ) @ V0op ) @ V14f ) @ V16t ) ) ) ) ) )
        & ! [V17f: $i] :
            ( ( mem @ V17f @ ( arr @ A_27h @ A_27i ) )
           => ! [V18g: $i] :
                ( ( mem @ V18g @ ( arr @ A_27i @ A_27b ) )
               => ! [V19s: $i] :
                    ( ( mem @ V19s @ ( arr @ A_27h @ bool ) )
                   => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27i @ A_27b ) @ V0op ) @ V18g ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27h @ A_27i ) @ V17f ) @ V19s ) )
                      = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27h @ A_27i ) @ V17f ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27h @ A_27b ) @ V0op ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27h @ A_27b @ A_27i ) @ V18g ) @ V17f ) ) @ V19s ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUPPORT__DELTA,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27b @ A_27a ) )
             => ! [V3a: $i] :
                  ( ( mem @ V3a @ A_27b )
                 => ( ( ap
                      @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op )
                        @ ( lam @ A_27b
                          @ ^ [V4x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V4x ) @ V3a ) ) @ ( ap @ V2f @ V4x ) ) @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op ) ) ) )
                      @ V1s )
                    = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ A_27b @ bool ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3a ) @ V1s ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V2f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V3a ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFINITE__SUPPORT__DELTA,axiom,
    ! [A_27a: del,A_27b: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27b @ bool ) )
     => ! [V1op: $i] :
          ( ( mem @ V1op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27b @ A_27a ) )
             => ! [V3a: $i] :
                  ( ( mem @ V3a @ A_27b )
                 => ( p
                    @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b )
                      @ ( ap
                        @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V1op )
                          @ ( lam @ A_27b
                            @ ^ [V4x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V4x ) @ V3a ) ) @ ( ap @ V2f @ V4x ) ) @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V1op ) ) ) )
                        @ V0s ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__SUPPORT,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V1f ) @ V2s ) ) @ V1f )
                = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V2s ) @ V1f ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__EXPAND__CASES,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V2s ) @ V1f )
                = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V1f ) @ V2s ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27b @ A_27a ) @ V0op ) @ V1f ) @ V2s ) ) @ V1f ) ) @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__CLAUSES__GEN,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ( ! [V1f: $i] :
              ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V1f )
                = ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) )
          & ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
             => ! [V3x: $i] :
                  ( ( mem @ V3x @ A_27a )
                 => ! [V4s: $i] :
                      ( ( mem @ V4s @ ( arr @ A_27a @ bool ) )
                     => ( ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
                          & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V2f ) @ V4s ) ) ) )
                       => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V3x ) @ V4s ) ) @ V2f )
                          = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V4s ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V4s ) @ V2f ) ) @ ( ap @ ( ap @ V0op @ ( ap @ V2f @ V3x ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V4s ) @ V2f ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__CLAUSES,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ V0op ) )
       => ( ! [V1f: $i] :
              ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) @ V1f )
                = ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op ) ) )
          & ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27b @ A_27a ) )
             => ! [V3x: $i] :
                  ( ( mem @ V3x @ A_27b )
                 => ! [V4s: $i] :
                      ( ( mem @ V4s @ ( arr @ A_27b @ bool ) )
                     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V4s ) )
                       => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V3x ) @ V4s ) ) @ V2f )
                          = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3x ) @ V4s ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V4s ) @ V2f ) ) @ ( ap @ ( ap @ V0op @ ( ap @ V2f @ V3x ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V4s ) @ V2f ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__UNION,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
           => ! [V2s: $i] :
                ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
               => ! [V3t: $i] :
                    ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2s ) )
                        & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V3t ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27b ) @ V2s ) @ V3t ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27b ) @ V2s ) @ V3t ) ) @ V1f )
                        = ( ap @ ( ap @ V0op @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V2s ) @ V1f ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V3t ) @ V1f ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__UNION__GEN,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2s: $i] :
                ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
               => ! [V3t: $i] :
                    ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V1f ) @ V2s ) ) )
                        & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V1f ) @ V3t ) ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V1f ) @ V2s ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V1f ) @ V3t ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V2s ) @ V3t ) ) @ V1f )
                        = ( ap @ ( ap @ V0op @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V2s ) @ V1f ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3t ) @ V1f ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__DIFF,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
           => ! [V2s: $i] :
                ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
               => ! [V3t: $i] :
                    ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2s ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ V3t ) @ V2s ) ) )
                     => ( ( ap @ ( ap @ V0op @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27b ) @ V2s ) @ V3t ) ) @ V1f ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V3t ) @ V1f ) )
                        = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V2s ) @ V1f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__DIFF__GEN,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2s: $i] :
                ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
               => ! [V3t: $i] :
                    ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V1f ) @ V2s ) ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V1f ) @ V3t ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V1f ) @ V2s ) ) ) )
                     => ( ( ap @ ( ap @ V0op @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V2s ) @ V3t ) ) @ V1f ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3t ) @ V1f ) )
                        = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V2s ) @ V1f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__INCL__EXCL,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ V0op ) )
       => ! [V1s: $i] :
            ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
           => ! [V2t: $i] :
                ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
               => ! [V3f: $i] :
                    ( ( mem @ V3f @ ( arr @ A_27b @ A_27a ) )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1s ) )
                        & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) ) )
                     => ( ( ap @ ( ap @ V0op @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V1s ) @ V3f ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V2t ) @ V3f ) )
                        = ( ap @ ( ap @ V0op @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27b ) @ V1s ) @ V2t ) ) @ V3f ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27b ) @ V1s ) @ V2t ) ) @ V3f ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__CLOSED,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1P: $i] :
            ( ( mem @ V1P @ ( arr @ A_27b @ bool ) )
           => ( ( ( p @ ( ap @ V1P @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) )
                & ! [V2x: $i] :
                    ( ( mem @ V2x @ A_27b )
                   => ! [V3y: $i] :
                        ( ( mem @ V3y @ A_27b )
                       => ( ( ( p @ ( ap @ V1P @ V2x ) )
                            & ( p @ ( ap @ V1P @ V3y ) ) )
                         => ( p @ ( ap @ V1P @ ( ap @ ( ap @ V0op @ V2x ) @ V3y ) ) ) ) ) ) )
             => ! [V4f: $i] :
                  ( ( mem @ V4f @ ( arr @ A_27a @ A_27b ) )
                 => ! [V5s: $i] :
                      ( ( mem @ V5s @ ( arr @ A_27a @ bool ) )
                     => ( ! [V6x: $i] :
                            ( ( mem @ V6x @ A_27a )
                           => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V5s ) )
                                & ( ( ap @ V4f @ V6x )
                                 != ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) )
                             => ( p @ ( ap @ V1P @ ( ap @ V4f @ V6x ) ) ) ) )
                       => ( p @ ( ap @ V1P @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V5s ) @ V4f ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__RELATED,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1R: $i] :
            ( ( mem @ V1R @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
           => ( ( ( p @ ( ap @ ( ap @ V1R @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) )
                & ! [V2x1: $i] :
                    ( ( mem @ V2x1 @ A_27b )
                   => ! [V3y1: $i] :
                        ( ( mem @ V3y1 @ A_27b )
                       => ! [V4x2: $i] :
                            ( ( mem @ V4x2 @ A_27b )
                           => ! [V5y2: $i] :
                                ( ( mem @ V5y2 @ A_27b )
                               => ( ( ( p @ ( ap @ ( ap @ V1R @ V2x1 ) @ V4x2 ) )
                                    & ( p @ ( ap @ ( ap @ V1R @ V3y1 ) @ V5y2 ) ) )
                                 => ( p @ ( ap @ ( ap @ V1R @ ( ap @ ( ap @ V0op @ V2x1 ) @ V3y1 ) ) @ ( ap @ ( ap @ V0op @ V4x2 ) @ V5y2 ) ) ) ) ) ) ) ) )
             => ! [V6f: $i] :
                  ( ( mem @ V6f @ ( arr @ A_27a @ A_27b ) )
                 => ! [V7g: $i] :
                      ( ( mem @ V7g @ ( arr @ A_27a @ A_27b ) )
                     => ! [V8s: $i] :
                          ( ( mem @ V8s @ ( arr @ A_27a @ bool ) )
                         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V8s ) )
                              & ! [V9x: $i] :
                                  ( ( mem @ V9x @ A_27a )
                                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V9x ) @ V8s ) )
                                   => ( p @ ( ap @ ( ap @ V1R @ ( ap @ V6f @ V9x ) ) @ ( ap @ V7g @ V9x ) ) ) ) ) )
                           => ( p @ ( ap @ ( ap @ V1R @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V8s ) @ V6f ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V8s ) @ V7g ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__EQ__NEUTRAL,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2s: $i] :
                ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
               => ( ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( ( ap @ V1f @ V3x )
                          = ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) ) )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V2s ) @ V1f )
                    = ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__SING,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V1f )
                  = ( ap @ V1f @ V2x ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__DELETE,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2s: $i] :
                ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
               => ! [V3a: $i] :
                    ( ( mem @ V3a @ A_27a )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                        & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3a ) @ V2s ) ) )
                     => ( ( ap @ ( ap @ V0op @ ( ap @ V1f @ V3a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V2s ) @ V3a ) ) @ V1f ) )
                        = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V2s ) @ V1f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__DELTA,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
           => ! [V2a: $i] :
                ( ( mem @ V2a @ A_27b )
               => ! [V3s: $i] :
                    ( ( mem @ V3s @ ( arr @ A_27b @ bool ) )
                   => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V3s )
                        @ ( lam @ A_27b
                          @ ^ [V4x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V4x ) @ V2a ) ) @ ( ap @ V1f @ V4x ) ) @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op ) ) ) )
                      = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V2a ) @ V3s ) ) @ ( ap @ V1f @ V2a ) ) @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V0op ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__IMAGE,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27c @ ( arr @ A_27c @ A_27c ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27c ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2g: $i] :
                ( ( mem @ V2g @ ( arr @ A_27b @ A_27c ) )
               => ! [V3s: $i] :
                    ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
                   => ( ! [V4x: $i] :
                          ( ( mem @ V4x @ A_27a )
                         => ! [V5y: $i] :
                              ( ( mem @ V5y @ A_27a )
                             => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V3s ) )
                                  & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V3s ) )
                                  & ( ( ap @ V1f @ V4x )
                                    = ( ap @ V1f @ V5y ) ) )
                               => ( V4x = V5y ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27c ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V1f ) @ V3s ) ) @ V2g )
                        = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27c ) @ V0op ) @ V3s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ A_27b ) @ V2g ) @ V1f ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__BIJECTION,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2p: $i] :
                ( ( mem @ V2p @ ( arr @ A_27a @ A_27a ) )
               => ! [V3s: $i] :
                    ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
                   => ( ( ! [V4x: $i] :
                            ( ( mem @ V4x @ A_27a )
                           => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V3s ) )
                             => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V2p @ V4x ) ) @ V3s ) ) ) )
                        & ! [V5y: $i] :
                            ( ( mem @ V5y @ A_27a )
                           => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V3s ) )
                             => ( p
                                @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
                                  @ ( lam @ A_27a
                                    @ ^ [V6x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V3s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V2p @ V6x ) ) @ V5y ) ) ) ) ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3s ) @ V1f )
                        = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27a ) @ V1f ) @ V2p ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__ITERATE__PRODUCT,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27c @ ( arr @ A_27c @ A_27c ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27c ) @ V0op ) )
       => ! [V1s: $i] :
            ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
           => ! [V2t: $i] :
                ( ( mem @ V2t @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
               => ! [V3x: $i] :
                    ( ( mem @ V3x @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                        & ! [V4i: $i] :
                            ( ( mem @ V4i @ A_27a )
                           => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4i ) @ V1s ) )
                             => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ V2t @ V4i ) ) ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27c ) @ V0op ) @ V1s )
                          @ ( lam @ A_27a
                            @ ^ [V5i: $i] : ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27c ) @ V0op ) @ ( ap @ V2t @ V5i ) ) @ ( ap @ V3x @ V5i ) ) ) )
                        = ( ap
                          @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ V0op )
                            @ ( 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
                                  @ ^ [V6i: $i] :
                                      ( lam @ A_27b
                                      @ ^ [V7j: $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 ) @ V6i ) @ V7j ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6i ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V7j ) @ ( ap @ V2t @ V6i ) ) ) ) ) ) ) ) )
                          @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c )
                            @ ( lam @ A_27a
                              @ ^ [V8i: $i] :
                                  ( lam @ A_27b
                                  @ ^ [V9j: $i] : ( ap @ ( ap @ V3x @ V8i ) @ V9j ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__EQ,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2g: $i] :
                ( ( mem @ V2g @ ( arr @ A_27a @ A_27b ) )
               => ! [V3s: $i] :
                    ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
                   => ( ! [V4x: $i] :
                          ( ( mem @ V4x @ A_27a )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V3s ) )
                           => ( ( ap @ V1f @ V4x )
                              = ( ap @ V2g @ V4x ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3s ) @ V1f )
                        = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3s ) @ V2g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__EQ__GENERAL,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27c @ ( arr @ A_27c @ A_27c ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27c ) @ V0op ) )
       => ! [V1s: $i] :
            ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
           => ! [V2t: $i] :
                ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
               => ! [V3f: $i] :
                    ( ( mem @ V3f @ ( arr @ A_27a @ A_27c ) )
                   => ! [V4g: $i] :
                        ( ( mem @ V4g @ ( arr @ A_27b @ A_27c ) )
                       => ! [V5h: $i] :
                            ( ( mem @ V5h @ ( arr @ A_27a @ A_27b ) )
                           => ( ( ! [V6y: $i] :
                                    ( ( mem @ V6y @ A_27b )
                                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V6y ) @ V2t ) )
                                     => ( p
                                        @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
                                          @ ( lam @ A_27a
                                            @ ^ [V7x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7x ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V5h @ V7x ) ) @ V6y ) ) ) ) ) ) )
                                & ! [V8x: $i] :
                                    ( ( mem @ V8x @ A_27a )
                                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V8x ) @ V1s ) )
                                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V5h @ V8x ) ) @ V2t ) )
                                        & ( ( ap @ V4g @ ( ap @ V5h @ V8x ) )
                                          = ( ap @ V3f @ V8x ) ) ) ) ) )
                             => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27c ) @ V0op ) @ V1s ) @ V3f )
                                = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27c ) @ V0op ) @ V2t ) @ V4g ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__EQ__GENERAL__INVERSES,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27c @ ( arr @ A_27c @ A_27c ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27c ) @ V0op ) )
       => ! [V1s: $i] :
            ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
           => ! [V2t: $i] :
                ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
               => ! [V3f: $i] :
                    ( ( mem @ V3f @ ( arr @ A_27a @ A_27c ) )
                   => ! [V4g: $i] :
                        ( ( mem @ V4g @ ( arr @ A_27b @ A_27c ) )
                       => ! [V5h: $i] :
                            ( ( mem @ V5h @ ( arr @ A_27a @ A_27b ) )
                           => ! [V6k: $i] :
                                ( ( mem @ V6k @ ( arr @ A_27b @ A_27a ) )
                               => ( ( ! [V7y: $i] :
                                        ( ( mem @ V7y @ A_27b )
                                       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V7y ) @ V2t ) )
                                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V6k @ V7y ) ) @ V1s ) )
                                            & ( ( ap @ V5h @ ( ap @ V6k @ V7y ) )
                                              = V7y ) ) ) )
                                    & ! [V8x: $i] :
                                        ( ( mem @ V8x @ A_27a )
                                       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V8x ) @ V1s ) )
                                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V5h @ V8x ) ) @ V2t ) )
                                            & ( ( ap @ V6k @ ( ap @ V5h @ V8x ) )
                                              = V8x )
                                            & ( ( ap @ V4g @ ( ap @ V5h @ V8x ) )
                                              = ( ap @ V3f @ V8x ) ) ) ) ) )
                                 => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27c ) @ V0op ) @ V1s ) @ V3f )
                                    = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27c ) @ V0op ) @ V2t ) @ V4g ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__INJECTION,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2p: $i] :
                ( ( mem @ V2p @ ( arr @ A_27a @ A_27a ) )
               => ! [V3s: $i] :
                    ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3s ) )
                        & ! [V4x: $i] :
                            ( ( mem @ V4x @ A_27a )
                           => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V3s ) )
                             => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V2p @ V4x ) ) @ V3s ) ) ) )
                        & ! [V5x: $i] :
                            ( ( mem @ V5x @ A_27a )
                           => ! [V6y: $i] :
                                ( ( mem @ V6y @ A_27a )
                               => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V3s ) )
                                    & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6y ) @ V3s ) )
                                    & ( ( ap @ V2p @ V5x )
                                      = ( ap @ V2p @ V6y ) ) )
                                 => ( V5x = V6y ) ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27a ) @ V1f ) @ V2p ) )
                        = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3s ) @ V1f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__UNION__NONZERO,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2s: $i] :
                ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
               => ! [V3t: $i] :
                    ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                        & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3t ) )
                        & ! [V4x: $i] :
                            ( ( mem @ V4x @ A_27a )
                           => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V2s ) @ V3t ) ) )
                             => ( ( ap @ V1f @ V4x )
                                = ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V2s ) @ V3t ) ) @ V1f )
                        = ( ap @ ( ap @ V0op @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V2s ) @ V1f ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3t ) @ V1f ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__OP,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
           => ! [V2g: $i] :
                ( ( mem @ V2g @ ( arr @ A_27b @ A_27a ) )
               => ! [V3s: $i] :
                    ( ( mem @ V3s @ ( arr @ A_27b @ bool ) )
                   => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V3s ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V3s )
                          @ ( lam @ A_27b
                            @ ^ [V4x: $i] : ( ap @ ( ap @ V0op @ ( ap @ V1f @ V4x ) ) @ ( ap @ V2g @ V4x ) ) ) )
                        = ( ap @ ( ap @ V0op @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V3s ) @ V1f ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27a ) @ V0op ) @ V3s ) @ V2g ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__SUPERSET,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2u: $i] :
                ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
               => ! [V3v: $i] :
                    ( ( mem @ V3v @ ( arr @ A_27a @ bool ) )
                   => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2u ) @ V3v ) )
                        & ! [V4x: $i] :
                            ( ( mem @ V4x @ A_27a )
                           => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V3v ) )
                                & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2u ) ) )
                             => ( ( ap @ V1f @ V4x )
                                = ( ap @ ( c_2Eiterate_2Eneutral @ A_27b ) @ V0op ) ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3v ) @ V1f )
                        = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V2u ) @ V1f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__IMAGE__NONZERO,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27c @ ( arr @ A_27c @ A_27c ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27c ) @ V0op ) )
       => ! [V1g: $i] :
            ( ( mem @ V1g @ ( arr @ A_27b @ A_27c ) )
           => ! [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
               => ! [V3s: $i] :
                    ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3s ) )
                        & ! [V4x: $i] :
                            ( ( mem @ V4x @ A_27a )
                           => ! [V5y: $i] :
                                ( ( mem @ V5y @ A_27a )
                               => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V3s ) )
                                    & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V3s ) )
                                    & ( V4x != V5y )
                                    & ( ( ap @ V2f @ V4x )
                                      = ( ap @ V2f @ V5y ) ) )
                                 => ( ( ap @ V1g @ ( ap @ V2f @ V4x ) )
                                    = ( ap @ ( c_2Eiterate_2Eneutral @ A_27c ) @ V0op ) ) ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27b @ A_27c ) @ V0op ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V2f ) @ V3s ) ) @ V1g )
                        = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27c ) @ V0op ) @ V3s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ A_27b ) @ V1g ) @ V2f ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__CASES,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1s: $i] :
            ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
           => ! [V2P: $i] :
                ( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
               => ! [V3f: $i] :
                    ( ( mem @ V3f @ ( arr @ A_27a @ A_27b ) )
                   => ! [V4g: $i] :
                        ( ( mem @ V4g @ ( arr @ A_27a @ A_27b ) )
                       => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                         => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V1s )
                              @ ( lam @ A_27a
                                @ ^ [V5x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ V2P @ V5x ) ) @ ( ap @ V3f @ V5x ) ) @ ( ap @ V4g @ V5x ) ) ) )
                            = ( ap
                              @ ( ap @ V0op
                                @ ( ap
                                  @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op )
                                    @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                      @ ( lam @ A_27a
                                        @ ^ [V6x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V6x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V1s ) ) @ ( ap @ V2P @ V6x ) ) ) ) ) )
                                  @ V3f ) )
                              @ ( ap
                                @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op )
                                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                    @ ( lam @ A_27a
                                      @ ^ [V7x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V7x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7x ) @ V1s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2P @ V7x ) ) ) ) ) ) )
                                @ V4g ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__OP__GEN,axiom,
    ! [A_27a: del,A_27b: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27b ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
           => ! [V2g: $i] :
                ( ( mem @ V2g @ ( arr @ A_27a @ A_27b ) )
               => ! [V3s: $i] :
                    ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
                   => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V1f ) @ V3s ) ) )
                        & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ A_27b ) @ V0op ) @ V2g ) @ V3s ) ) ) )
                     => ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3s )
                          @ ( lam @ A_27a
                            @ ^ [V4x: $i] : ( ap @ ( ap @ V0op @ ( ap @ V1f @ V4x ) ) @ ( ap @ V2g @ V4x ) ) ) )
                        = ( ap @ ( ap @ V0op @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3s ) @ V1f ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ A_27b ) @ V0op ) @ V3s ) @ V2g ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__CLAUSES__NUMSEG,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
     => ! [V1op: $i] :
          ( ( mem @ V1op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
         => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ V1op ) )
           => ( ! [V2m: tp__ty_2Enum_2Enum] :
                  ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ ty_2Enum_2Enum @ A_27a ) @ V1op ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0f )
                  = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Eiterate_2Eneutral @ A_27a ) @ V1op ) ) )
              & ! [V3m: tp__ty_2Enum_2Enum,V4n: tp__ty_2Enum_2Enum] :
                  ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ ty_2Enum_2Enum @ A_27a ) @ V1op ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) @ V0f )
                  = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) @ ( ap @ ( ap @ V1op @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ ty_2Enum_2Enum @ A_27a ) @ V1op ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ V0f ) ) @ ( ap @ V0f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ ty_2Enum_2Enum @ A_27a ) @ V1op ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ V0f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EITERATE__PAIR,axiom,
    ! [A_27a: del,V0op: $i] :
      ( ( mem @ V0op @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
     => ( ( p @ ( ap @ ( c_2Eiterate_2Emonoidal @ A_27a ) @ V0op ) )
       => ! [V1f: $i] :
            ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
           => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
                ( ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ ty_2Enum_2Enum @ A_27a ) @ V0op ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V1f )
                = ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Eiterate @ ty_2Enum_2Enum @ A_27a ) @ V0op ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4i: $i] : ( ap @ ( ap @ V0op @ ( ap @ V1f @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V4i ) ) ) @ ( ap @ V1f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V4i ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eiterate_2Ensum__def,axiom,
    ! [A_27a: del] :
      ( ( c_2Eiterate_2Ensum @ A_27a )
      = ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ ty_2Enum_2Enum ) @ c_2Earithmetic_2E_2B ) ) ).

thf(conj_thm_2Eiterate_2ENEUTRAL__ADD,axiom,
    ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Eiterate_2Eneutral @ ty_2Enum_2Enum ) @ c_2Earithmetic_2E_2B ) )
    = fo__c_2Enum_2E0 ) ).

thf(conj_thm_2Eiterate_2ENEUTRAL__MUL,axiom,
    ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Eiterate_2Eneutral @ ty_2Enum_2Enum ) @ c_2Earithmetic_2E_2A ) )
    = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EMONOIDAL__ADD,axiom,
    p @ ( ap @ ( c_2Eiterate_2Emonoidal @ ty_2Enum_2Enum ) @ c_2Earithmetic_2E_2B ) ).

thf(conj_thm_2Eiterate_2EMONOIDAL__MUL,axiom,
    p @ ( ap @ ( c_2Eiterate_2Emonoidal @ ty_2Enum_2Enum ) @ c_2Earithmetic_2E_2A ) ).

thf(conj_thm_2Eiterate_2ENSUM__DEGENERATE,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ~ ( p
                @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                    @ ( lam @ A_27a
                      @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ V0f @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) )
           => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) )
              = fo__c_2Enum_2E0 ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__CLAUSES,axiom,
    ! [A_27a: del,A_27b: del] :
      ( ! [V0f: $i] :
          ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0f ) )
            = fo__c_2Enum_2E0 ) )
      & ! [V1x: $i] :
          ( ( mem @ V1x @ A_27b )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
             => ! [V3s: $i] :
                  ( ( mem @ V3s @ ( arr @ A_27b @ bool ) )
                 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V3s ) )
                   => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V1x ) @ V3s ) ) @ V2f ) )
                      = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V1x ) @ V3s ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ V3s ) @ V2f ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V2f @ V1x ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ V3s ) @ V2f ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__UNION,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2t ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V1s ) @ V2t ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t ) ) @ V0f ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2t ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__DIFF,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2t ) @ V1s ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1s ) @ V2t ) ) @ V0f ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2t ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__INCL__EXCL,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s ) @ V2f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1t ) @ V2f ) ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) @ V2f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) @ V2f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__SUPPORT,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ ty_2Enum_2Enum ) @ c_2Earithmetic_2E_2B ) @ V0f ) @ V1s ) ) @ V0f ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__ADD,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
               => ( ( surj__ty_2Enum_2Enum
                    @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s )
                      @ ( lam @ A_27a
                        @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__ADD__GEN,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p
                    @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
                      @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                        @ ( lam @ A_27a
                          @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ V0f @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) )
                  & ( 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_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ V1g @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) )
               => ( ( surj__ty_2Enum_2Enum
                    @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s )
                      @ ( lam @ A_27a
                        @ ^ [V5x: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V0f @ V5x ) ) @ ( ap @ V1g @ V5x ) ) ) ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__EQ__0,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                 => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V2x ) )
                    = fo__c_2Enum_2E0 ) ) )
           => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) )
              = fo__c_2Enum_2E0 ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__0,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( surj__ty_2Enum_2Enum
          @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s )
            @ ( lam @ A_27a
              @ ^ [V1n: $i] : ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
        = fo__c_2Enum_2E0 ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__LMUL,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1c: tp__ty_2Enum_2Enum,V2s: $i] :
          ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
         => ( ( surj__ty_2Enum_2Enum
              @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s )
                @ ( lam @ A_27a
                  @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ ( ap @ V0f @ V3x ) ) ) ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__RMUL,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1c: tp__ty_2Enum_2Enum,V2s: $i] :
          ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
         => ( ( surj__ty_2Enum_2Enum
              @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s )
                @ ( lam @ A_27a
                  @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ V0f @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) ) ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__LE,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__LT,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) )
                  & ? [V4x: $i] :
                      ( ( mem @ V4x @ A_27a )
                      & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) )
                      & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V0f @ V4x ) ) @ ( ap @ V1g @ V4x ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__LT__ALL,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ( V2s
                   != ( c_2Epred__set_2EEMPTY @ A_27a ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__EQ,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                     => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V3x ) )
                        = ( surj__ty_2Enum_2Enum @ ( ap @ V1g @ V3x ) ) ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__CONST,axiom,
    ! [A_27a: del,V0c: tp__ty_2Enum_2Enum,V1s: $i] :
      ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
       => ( ( surj__ty_2Enum_2Enum
            @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s )
              @ ( lam @ A_27a
                @ ^ [V2n: $i] : ( inj__ty_2Enum_2Enum @ V0c ) ) ) )
          = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__POS__BOUND,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1b: tp__ty_2Enum_2Enum,V2s: $i] :
          ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
              & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
           => ! [V3x: $i] :
                ( ( mem @ V3x @ A_27a )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0f @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__EQ__0__IFF,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
           => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) )
                = fo__c_2Enum_2E0 )
            <=> ! [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                   => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V2x ) )
                      = fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__POS__LT,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
              & ? [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                  & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                  & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V0f @ V2x ) ) ) ) )
           => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__POS__LT__ALL,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
              & ( V0s
               != ( c_2Epred__set_2EEMPTY @ A_27a ) )
              & ! [V2i: $i] :
                  ( ( mem @ V2i @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2i ) @ V0s ) )
                   => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V1f @ V2i ) ) ) ) ) )
           => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s ) @ V1f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__DELETE,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2a: $i] :
              ( ( mem @ V2a @ A_27a )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2a ) @ V1s ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V0f @ V2a ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V2a ) ) @ V0f ) ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__SING,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V0f ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V1x ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__DELTA,axiom,
    ! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1s: $i] :
      ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
     => ! [V2a: $i] :
          ( ( mem @ V2a @ A_27a )
         => ( ( surj__ty_2Enum_2Enum
              @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s )
                @ ( lam @ A_27a
                  @ ^ [V3x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2a ) @ V1s ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__SWAP,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ ty_2Enum_2Enum ) ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) ) )
               => ( ( surj__ty_2Enum_2Enum
                    @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s )
                      @ ( lam @ A_27a
                        @ ^ [V3i: $i] : ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ V2t ) @ ( ap @ V0f @ V3i ) ) ) ) )
                  = ( surj__ty_2Enum_2Enum
                    @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ V2t )
                      @ ( lam @ A_27b
                        @ ^ [V4j: $i] :
                            ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s )
                            @ ( lam @ A_27a
                              @ ^ [V5i: $i] : ( ap @ ( ap @ V0f @ V5i ) @ V4j ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__IMAGE,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
         => ! [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 ) ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) ) @ V1g ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ty_2Enum_2Enum @ A_27b ) @ V1g ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__SUPERSET,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1u: $i] :
          ( ( mem @ V1u @ ( arr @ A_27a @ bool ) )
         => ! [V2v: $i] :
              ( ( mem @ V2v @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1u ) @ V2v ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2v ) )
                          & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1u ) ) )
                       => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V3x ) )
                          = fo__c_2Enum_2E0 ) ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2v ) @ V0f ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1u ) @ V0f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__UNION__RZERO,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1u: $i] :
          ( ( mem @ V1u @ ( arr @ A_27a @ bool ) )
         => ! [V2v: $i] :
              ( ( mem @ V2v @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1u ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2v ) )
                          & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1u ) ) )
                       => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V3x ) )
                          = fo__c_2Enum_2E0 ) ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1u ) @ V2v ) ) @ V0f ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1u ) @ V0f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__UNION__LZERO,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1u: $i] :
          ( ( mem @ V1u @ ( arr @ A_27a @ bool ) )
         => ! [V2v: $i] :
              ( ( mem @ V2v @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2v ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1u ) )
                          & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2v ) ) )
                       => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V3x ) )
                          = fo__c_2Enum_2E0 ) ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1u ) @ V2v ) ) @ V0f ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2v ) @ V0f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__RESTRICT,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
           => ( ( surj__ty_2Enum_2Enum
                @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s )
                  @ ( lam @ A_27a
                    @ ^ [V2x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) ) @ ( ap @ V0f @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
              = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__BOUND,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2b: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V1f @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s ) @ V1f ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__BOUND__GEN,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2b: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ( V0s
                 != ( c_2Epred__set_2EEMPTY @ A_27a ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V1f @ V3x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s ) @ V1f ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__BOUND__LT,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2b: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V1f @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) )
                & ? [V4x: $i] :
                    ( ( mem @ V4x @ A_27a )
                    & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V0s ) )
                    & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V1f @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s ) @ V1f ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__BOUND__LT__ALL,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2b: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ( V0s
                 != ( c_2Epred__set_2EEMPTY @ A_27a ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V1f @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s ) @ V1f ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__BOUND__LT__GEN,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2b: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ( V0s
                 != ( c_2Epred__set_2EEMPTY @ A_27a ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V1f @ V3x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s ) @ V1f ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__UNION__EQ,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
             => ! [V3u: $i] :
                  ( ( mem @ V3u @ ( arr @ A_27a @ bool ) )
                 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3u ) )
                      & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V2t )
                        = ( c_2Epred__set_2EEMPTY @ A_27a ) )
                      & ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t )
                        = V3u ) )
                   => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2t ) @ V0f ) ) )
                      = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V3u ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__EQ__SUPERSET,axiom,
    ! [A_27a: del,V0g: $i] :
      ( ( mem @ V0g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3t ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V3t ) @ V2s ) )
                      & ! [V4x: $i] :
                          ( ( mem @ V4x @ A_27a )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V3t ) )
                           => ( ( surj__ty_2Enum_2Enum @ ( ap @ V1f @ V4x ) )
                              = ( surj__ty_2Enum_2Enum @ ( ap @ V0g @ V4x ) ) ) ) )
                      & ! [V5x: $i] :
                          ( ( mem @ V5x @ A_27a )
                         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V2s ) )
                              & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V3t ) ) )
                           => ( ( surj__ty_2Enum_2Enum @ ( ap @ V1f @ V5x ) )
                              = fo__c_2Enum_2E0 ) ) ) )
                   => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1f ) )
                      = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V3t ) @ V0g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__RESTRICT__SET,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
             => ( ( surj__ty_2Enum_2Enum
                  @ ( ap
                    @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a )
                      @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                        @ ( lam @ A_27a
                          @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) ) @ ( ap @ V0P @ V3x ) ) ) ) ) )
                    @ V2f ) )
                = ( surj__ty_2Enum_2Enum
                  @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s )
                    @ ( lam @ A_27a
                      @ ^ [V4x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ V0P @ V4x ) ) @ ( ap @ V2f @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__NSUM__RESTRICT,axiom,
    ! [A_27a: del,A_27b: del,V0R: $i] :
      ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ A_27b @ ty_2Enum_2Enum ) ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
                 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                      & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V3t ) ) )
                   => ( ( surj__ty_2Enum_2Enum
                        @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s )
                          @ ( lam @ A_27a
                            @ ^ [V4x: $i] :
                                ( ap
                                @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b )
                                  @ ( 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 @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V5y ) @ V3t ) ) @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) ) ) ) ) )
                                @ ( lam @ A_27b
                                  @ ^ [V6y: $i] : ( ap @ ( ap @ V1f @ V4x ) @ V6y ) ) ) ) ) )
                      = ( surj__ty_2Enum_2Enum
                        @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ V3t )
                          @ ( lam @ A_27b
                            @ ^ [V7y: $i] :
                                ( ap
                                @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a )
                                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                    @ ( lam @ A_27a
                                      @ ^ [V8x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V8x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V8x ) @ V2s ) ) @ ( ap @ ( ap @ V0R @ V8x ) @ V7y ) ) ) ) ) )
                                @ ( lam @ A_27a
                                  @ ^ [V9x: $i] : ( ap @ ( ap @ V1f @ V9x ) @ V7y ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ECARD__EQ__NSUM,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
       => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) )
          = ( surj__ty_2Enum_2Enum
            @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s )
              @ ( lam @ A_27a
                @ ^ [V1x: $i] : ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__MULTICOUNT__GEN,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 ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
             => ! [V3k: $i] :
                  ( ( mem @ V3k @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
                 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                      & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) )
                      & ! [V4j: $i] :
                          ( ( mem @ V4j @ A_27b )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4j ) @ V2t ) )
                           => ( ( surj__ty_2Enum_2Enum
                                @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a )
                                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                    @ ( lam @ A_27a
                                      @ ^ [V5i: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V5i ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5i ) @ V1s ) ) @ ( ap @ ( ap @ V0R @ V5i ) @ V4j ) ) ) ) ) ) )
                              = ( surj__ty_2Enum_2Enum @ ( ap @ V3k @ V4j ) ) ) ) ) )
                   => ( ( surj__ty_2Enum_2Enum
                        @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s )
                          @ ( lam @ A_27a
                            @ ^ [V6i: $i] :
                                ( ap @ ( c_2Epred__set_2ECARD @ A_27b )
                                @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27b )
                                  @ ( lam @ A_27b
                                    @ ^ [V7j: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ V7j ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V7j ) @ V2t ) ) @ ( ap @ ( ap @ V0R @ V6i ) @ V7j ) ) ) ) ) ) ) ) )
                      = ( surj__ty_2Enum_2Enum
                        @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ V2t )
                          @ ( lam @ A_27b
                            @ ^ [V8i: $i] : ( ap @ V3k @ V8i ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__MULTICOUNT,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 ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
             => ! [V3k: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                    & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) )
                    & ! [V4j: $i] :
                        ( ( mem @ V4j @ A_27b )
                       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4j ) @ V2t ) )
                         => ( ( surj__ty_2Enum_2Enum
                              @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a )
                                @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                  @ ( lam @ A_27a
                                    @ ^ [V5i: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V5i ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5i ) @ V1s ) ) @ ( ap @ ( ap @ V0R @ V5i ) @ V4j ) ) ) ) ) ) )
                            = V3k ) ) ) )
                 => ( ( surj__ty_2Enum_2Enum
                      @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s )
                        @ ( lam @ A_27a
                          @ ^ [V6i: $i] :
                              ( ap @ ( c_2Epred__set_2ECARD @ A_27b )
                              @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27b )
                                @ ( lam @ A_27b
                                  @ ^ [V7j: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ V7j ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V7j ) @ V2t ) ) @ ( ap @ ( ap @ V0R @ V6i ) @ V7j ) ) ) ) ) ) ) ) )
                    = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3k ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V2t ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__IMAGE__GEN,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1g ) )
                  = ( surj__ty_2Enum_2Enum
                    @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) )
                      @ ( lam @ A_27b
                        @ ^ [V3y: $i] :
                            ( ap
                            @ ( ap @ ( c_2Eiterate_2Ensum @ 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_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V4x ) ) @ V3y ) ) ) ) ) )
                            @ V1g ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__GROUP,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
                 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) ) @ V3t ) ) )
                   => ( ( surj__ty_2Enum_2Enum
                        @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ V3t )
                          @ ( lam @ A_27b
                            @ ^ [V4y: $i] :
                                ( ap
                                @ ( ap @ ( c_2Eiterate_2Ensum @ 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_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V5x ) ) @ V4y ) ) ) ) ) )
                                @ V1g ) ) ) )
                      = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__SUBSET,axiom,
    ! [A_27a: del,V0u: $i] :
      ( ( mem @ V0u @ ( arr @ A_27a @ bool ) )
     => ! [V1v: $i] :
          ( ( mem @ V1v @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0u ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1v ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0u ) @ V1v ) ) )
                       => ( ( surj__ty_2Enum_2Enum @ ( ap @ V2f @ V3x ) )
                          = fo__c_2Enum_2E0 ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0u ) @ V2f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1v ) @ V2f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__SUBSET__SIMPLE,axiom,
    ! [A_27a: del,V0u: $i] :
      ( ( mem @ V0u @ ( arr @ A_27a @ bool ) )
     => ! [V1v: $i] :
          ( ( mem @ V1v @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1v ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0u ) @ V1v ) ) )
               => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0u ) @ V2f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1v ) @ V2f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__LE__GEN,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) )
                  & ( 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_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ V1g @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__IMAGE__NONZERO,axiom,
    ! [A_27a: del,A_27b: del,V0d: $i] :
      ( ( mem @ V0d @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
     => ! [V1i: $i] :
          ( ( mem @ V1i @ ( arr @ A_27a @ A_27b ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ! [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 ) )
                              & ( V3x != V4y )
                              & ( ( ap @ V1i @ V3x )
                                = ( ap @ V1i @ V4y ) ) )
                           => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0d @ ( ap @ V1i @ V3x ) ) )
                              = fo__c_2Enum_2E0 ) ) ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V1i ) @ V2s ) ) @ V0d ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ty_2Enum_2Enum @ A_27b ) @ V0d ) @ V1i ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__BIJECTION,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1p: $i] :
          ( ( mem @ V1p @ ( arr @ A_27a @ A_27a ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V1p @ V3x ) ) @ V2s ) ) ) )
                  & ! [V4y: $i] :
                      ( ( mem @ V4y @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V2s ) )
                       => ( 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 ) @ V2s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V1p @ V5x ) ) @ V4y ) ) ) ) ) ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ty_2Enum_2Enum @ A_27a ) @ V0f ) @ V1p ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__NSUM__PRODUCT,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 ) ) )
         => ! [V2x: $i] :
              ( ( mem @ V2x @ ( arr @ A_27a @ ( arr @ A_27b @ ty_2Enum_2Enum ) ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                  & ! [V3i: $i] :
                      ( ( mem @ V3i @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3i ) @ V0s ) )
                       => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ V1t @ V3i ) ) ) ) ) )
               => ( ( surj__ty_2Enum_2Enum
                    @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s )
                      @ ( lam @ A_27a
                        @ ^ [V4i: $i] : ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ ( ap @ V1t @ V4i ) ) @ ( ap @ V2x @ V4i ) ) ) ) )
                  = ( surj__ty_2Enum_2Enum
                    @ ( ap
                      @ ( ap @ ( c_2Eiterate_2Ensum @ ( 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
                              @ ^ [V5i: $i] :
                                  ( lam @ A_27b
                                  @ ^ [V6j: $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 ) @ V5i ) @ V6j ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5i ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V6j ) @ ( ap @ V1t @ V5i ) ) ) ) ) ) ) ) )
                      @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ty_2Enum_2Enum )
                        @ ( lam @ A_27a
                          @ ^ [V7i: $i] :
                              ( lam @ A_27b
                              @ ^ [V8j: $i] : ( ap @ ( ap @ V2x @ V7i ) @ V8j ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__EQ__GENERAL,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 @ ty_2Enum_2Enum ) )
             => ! [V3g: $i] :
                  ( ( mem @ V3g @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
                 => ! [V4h: $i] :
                      ( ( mem @ V4h @ ( arr @ A_27a @ A_27b ) )
                     => ( ( ! [V5y: $i] :
                              ( ( mem @ V5y @ A_27b )
                             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V5y ) @ V1t ) )
                               => ( p
                                  @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
                                    @ ( lam @ A_27a
                                      @ ^ [V6x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V4h @ V6x ) ) @ V5y ) ) ) ) ) ) )
                          & ! [V7x: $i] :
                              ( ( mem @ V7x @ A_27a )
                             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7x ) @ V0s ) )
                               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V4h @ V7x ) ) @ V1t ) )
                                  & ( ( surj__ty_2Enum_2Enum @ ( ap @ V3g @ ( ap @ V4h @ V7x ) ) )
                                    = ( surj__ty_2Enum_2Enum @ ( ap @ V2f @ V7x ) ) ) ) ) ) )
                       => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s ) @ V2f ) )
                          = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ V1t ) @ V3g ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__EQ__GENERAL__INVERSES,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 @ ty_2Enum_2Enum ) )
             => ! [V3g: $i] :
                  ( ( mem @ V3g @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
                 => ! [V4h: $i] :
                      ( ( mem @ V4h @ ( arr @ A_27a @ A_27b ) )
                     => ! [V5k: $i] :
                          ( ( mem @ V5k @ ( arr @ A_27b @ A_27a ) )
                         => ( ( ! [V6y: $i] :
                                  ( ( mem @ V6y @ A_27b )
                                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V6y ) @ V1t ) )
                                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V5k @ V6y ) ) @ V0s ) )
                                      & ( ( ap @ V4h @ ( ap @ V5k @ V6y ) )
                                        = V6y ) ) ) )
                              & ! [V7x: $i] :
                                  ( ( mem @ V7x @ A_27a )
                                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7x ) @ V0s ) )
                                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V4h @ V7x ) ) @ V1t ) )
                                      & ( ( ap @ V5k @ ( ap @ V4h @ V7x ) )
                                        = V7x )
                                      & ( ( surj__ty_2Enum_2Enum @ ( ap @ V3g @ ( ap @ V4h @ V7x ) ) )
                                        = ( surj__ty_2Enum_2Enum @ ( ap @ V2f @ V7x ) ) ) ) ) ) )
                           => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s ) @ V2f ) )
                              = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27b ) @ V1t ) @ V3g ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__INJECTION,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1p: $i] :
          ( ( mem @ V1p @ ( arr @ A_27a @ A_27a ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V1p @ V3x ) ) @ V2s ) ) ) )
                  & ! [V4x: $i] :
                      ( ( mem @ V4x @ A_27a )
                     => ! [V5y: $i] :
                          ( ( mem @ V5y @ A_27a )
                         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V2s ) )
                              & ( ( ap @ V1p @ V4x )
                                = ( ap @ V1p @ V5y ) ) )
                           => ( V4x = V5y ) ) ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ty_2Enum_2Enum @ A_27a ) @ V0f ) @ V1p ) ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__UNION__NONZERO,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2t ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V2t ) ) )
                       => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V3x ) )
                          = fo__c_2Enum_2E0 ) ) ) )
               => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t ) ) @ V0f ) )
                  = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2t ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__BIGUNION__NONZERO,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( arr @ A_27a @ bool ) ) @ V1s ) )
              & ! [V2t: $i] :
                  ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2t ) @ V1s ) )
                   => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2t ) ) ) )
              & ! [V3t1: $i] :
                  ( ( mem @ V3t1 @ ( arr @ A_27a @ bool ) )
                 => ! [V4t2: $i] :
                      ( ( mem @ V4t2 @ ( arr @ A_27a @ bool ) )
                     => ! [V5x: $i] :
                          ( ( mem @ V5x @ A_27a )
                         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V3t1 ) @ V1s ) )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V4t2 ) @ V1s ) )
                              & ( V3t1 != V4t2 )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V3t1 ) )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V4t2 ) ) )
                           => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V5x ) )
                              = fo__c_2Enum_2E0 ) ) ) ) ) )
           => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1s ) ) @ V0f ) )
              = ( surj__ty_2Enum_2Enum
                @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ( arr @ A_27a @ bool ) ) @ V1s )
                  @ ( lam @ ( arr @ A_27a @ bool )
                    @ ^ [V6t: $i] : ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V6t ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__CASES,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1P: $i] :
          ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
             => ! [V3g: $i] :
                  ( ( mem @ V3g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
                 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                   => ( ( surj__ty_2Enum_2Enum
                        @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V0s )
                          @ ( lam @ A_27a
                            @ ^ [V4x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ V1P @ V4x ) ) @ ( ap @ V2f @ V4x ) ) @ ( ap @ V3g @ V4x ) ) ) ) )
                      = ( surj__ty_2Enum_2Enum
                        @ ( ap
                          @ ( ap @ c_2Earithmetic_2E_2B
                            @ ( ap
                              @ ( ap @ ( c_2Eiterate_2Ensum @ 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 ) @ V0s ) ) @ ( ap @ V1P @ V5x ) ) ) ) ) )
                              @ V2f ) )
                          @ ( ap
                            @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a )
                              @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                @ ( lam @ A_27a
                                  @ ^ [V6x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V6x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V0s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1P @ V6x ) ) ) ) ) ) )
                            @ V3g ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__CLOSED,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
                  & ! [V3x: tp__ty_2Enum_2Enum,V4y: tp__ty_2Enum_2Enum] :
                      ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3x ) ) )
                        & ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V4y ) ) ) )
                     => ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V4y ) ) ) ) )
                  & ! [V5a: $i] :
                      ( ( mem @ V5a @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5a ) @ V2s ) )
                       => ( p @ ( ap @ V0P @ ( ap @ V1f @ V5a ) ) ) ) ) )
               => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V1f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__ADD__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
         => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ( surj__ty_2Enum_2Enum
                @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V0f @ V4i ) ) @ ( ap @ V1g @ V4i ) ) ) ) )
              = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V1g ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__LE__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
         => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ! [V4i: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) )
                    & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
                 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V4i ) ) ) @ ( ap @ V1g @ ( inj__ty_2Enum_2Enum @ V4i ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V1g ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__EQ__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
         => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ! [V4i: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) )
                    & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
                 => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V4i ) ) )
                    = ( surj__ty_2Enum_2Enum @ ( ap @ V1g @ ( inj__ty_2Enum_2Enum @ V4i ) ) ) ) )
             => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) )
                = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V1g ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__CONST__NUMSEG,axiom,
    ! [V0c: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
      ( ( surj__ty_2Enum_2Enum
        @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
          @ ( lam @ ty_2Enum_2Enum
            @ ^ [V3n: $i] : ( inj__ty_2Enum_2Enum @ V0c ) ) ) )
      = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__EQ__0__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ! [V3i: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) )
                & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
             => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V3i ) ) )
                = fo__c_2Enum_2E0 ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = fo__c_2Enum_2E0 ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__EQ__0__IFF__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = fo__c_2Enum_2E0 )
        <=> ! [V3i: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) )
                & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
             => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V3i ) ) )
                = fo__c_2Enum_2E0 ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__TRIV__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = fo__c_2Enum_2E0 ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__SING__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1n: tp__ty_2Enum_2Enum] :
          ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V0f ) )
          = ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__CLAUSES__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ( ! [V1m: tp__ty_2Enum_2Enum] :
            ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0f ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
        & ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
            ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ V0f ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) ) @ ( ap @ V0f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__SWAP__NUMSEG,axiom,
    ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum,V3d: tp__ty_2Enum_2Enum,V4f: $i] :
      ( ( mem @ V4f @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
     => ( ( surj__ty_2Enum_2Enum
          @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
            @ ( lam @ ty_2Enum_2Enum
              @ ^ [V5i: $i] : ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2c ) ) @ ( inj__ty_2Enum_2Enum @ V3d ) ) ) @ ( ap @ V4f @ V5i ) ) ) ) )
        = ( surj__ty_2Enum_2Enum
          @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2c ) ) @ ( inj__ty_2Enum_2Enum @ V3d ) ) )
            @ ( lam @ ty_2Enum_2Enum
              @ ^ [V6j: $i] :
                  ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V7i: $i] : ( ap @ ( ap @ V4f @ V7i ) @ V6j ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__ADD__SPLIT,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3p: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) ) @ V0f ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__OFFSET,axiom,
    ! [V0p: tp__ty_2Enum_2Enum,V1f: $i] :
      ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
          ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) ) @ V1f ) )
          = ( surj__ty_2Enum_2Enum
            @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V4i: $i] : ( ap @ V1f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V4i ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__OFFSET__0,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = ( surj__ty_2Enum_2Enum
              @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V3i: $i] : ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3i ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__CLAUSES__LEFT,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__CLAUSES__RIGHT,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1m: tp__ty_2Enum_2Enum,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 ) ) )
            & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V0f ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENSUM__PAIR,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V0f ) )
          = ( surj__ty_2Enum_2Enum
            @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3i: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V3i ) ) ) @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V3i ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EMOD__NSUM__MOD,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1n: tp__ty_2Enum_2Enum,V2s: $i] :
          ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
              & ( V1n != fo__c_2Enum_2E0 ) )
           => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s ) @ V0f ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
              = ( surj__ty_2Enum_2Enum
                @ ( ap
                  @ ( ap @ c_2Earithmetic_2EMOD
                    @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V2s )
                      @ ( lam @ A_27a
                        @ ^ [V3i: $i] : ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ V0f @ V3i ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
                  @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EMOD__NSUM__MOD__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
          ( ( V3n != fo__c_2Enum_2E0 )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) @ V0f ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
            = ( surj__ty_2Enum_2Enum
              @ ( ap
                @ ( ap @ c_2Earithmetic_2EMOD
                  @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ V0f @ V4i ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) )
                @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ECARD__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 ) )
          & ! [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 ) ) ) )
          & ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
             => ! [V3u: $i] :
                  ( ( mem @ V3u @ ( arr @ A_27a @ bool ) )
                 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2t ) @ V0s ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V3u ) @ V0s ) )
                      & ( V2t != V3u ) )
                   => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V2t ) @ V3u )
                      = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) )
       => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0s ) ) )
          = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ( arr @ A_27a @ bool ) ) @ V0s ) @ ( c_2Epred__set_2ECARD @ A_27a ) ) ) ) ) ) ).

thf(ax_thm_2Eiterate_2Esum__def,axiom,
    ! [A_27a: del] :
      ( ( c_2Eiterate_2ESum @ A_27a )
      = ( ap @ ( c_2Eiterate_2Eiterate @ A_27a @ ty_2Erealax_2Ereal ) @ c_2Erealax_2Ereal__add ) ) ).

thf(conj_thm_2Eiterate_2ENEUTRAL__REAL__ADD,axiom,
    ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Eiterate_2Eneutral @ ty_2Erealax_2Ereal ) @ c_2Erealax_2Ereal__add ) )
    = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).

thf(conj_thm_2Eiterate_2ENEUTRAL__REAL__MUL,axiom,
    ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Eiterate_2Eneutral @ ty_2Erealax_2Ereal ) @ c_2Erealax_2Ereal__mul ) )
    = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EMONOIDAL__REAL__ADD,axiom,
    p @ ( ap @ ( c_2Eiterate_2Emonoidal @ ty_2Erealax_2Ereal ) @ c_2Erealax_2Ereal__add ) ).

thf(conj_thm_2Eiterate_2EMONOIDAL__REAL__MUL,axiom,
    p @ ( ap @ ( c_2Eiterate_2Emonoidal @ ty_2Erealax_2Ereal ) @ c_2Erealax_2Ereal__mul ) ).

thf(conj_thm_2Eiterate_2ESUM__DEGENERATE,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ~ ( p
                @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                    @ ( lam @ A_27a
                      @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal ) @ ( ap @ V0f @ V2x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) )
           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) )
              = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__CLAUSES,axiom,
    ! [A_27a: del,A_27b: del] :
      ( ! [V0f: $i] :
          ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
      & ! [V1x: $i] :
          ( ( mem @ V1x @ A_27b )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) )
             => ! [V3s: $i] :
                  ( ( mem @ V3s @ ( arr @ A_27b @ bool ) )
                 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V3s ) )
                   => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V1x ) @ V3s ) ) @ V2f ) )
                      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V1x ) @ V3s ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ V3s ) @ V2f ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ V2f @ V1x ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ V3s ) @ V2f ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__UNION,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2t ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V1s ) @ V2t ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t ) ) @ V0f ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2t ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__DIFF,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2t ) @ V1s ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1s ) @ V2t ) ) @ V0f ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2t ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__INCL__EXCL,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ V2f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1t ) @ V2f ) ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) @ V2f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) @ V2f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SUPPORT,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eiterate_2Esupport @ A_27a @ ty_2Erealax_2Ereal ) @ c_2Erealax_2Ereal__add ) @ V0f ) @ V1s ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__ADD,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
               => ( ( surj__ty_2Erealax_2Ereal
                    @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s )
                      @ ( lam @ A_27a
                        @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__ADD__GEN,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p
                    @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
                      @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                        @ ( lam @ A_27a
                          @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal ) @ ( ap @ V0f @ V3x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) )
                  & ( 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_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal ) @ ( ap @ V1g @ V4x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal
                    @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s )
                      @ ( lam @ A_27a
                        @ ^ [V5x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ V0f @ V5x ) ) @ ( ap @ V1g @ V5x ) ) ) ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__EQ__0,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                 => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ V2x ) )
                    = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) )
           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) )
              = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__0,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( surj__ty_2Erealax_2Ereal
          @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s )
            @ ( lam @ A_27a
              @ ^ [V1n: $i] : ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__LMUL,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1c: tp__ty_2Erealax_2Ereal,V2s: $i] :
          ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
         => ( ( surj__ty_2Erealax_2Ereal
              @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s )
                @ ( lam @ A_27a
                  @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1c ) ) @ ( ap @ V0f @ V3x ) ) ) ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1c ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__RMUL,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1c: tp__ty_2Erealax_2Ereal,V2s: $i] :
          ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
         => ( ( surj__ty_2Erealax_2Ereal
              @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s )
                @ ( lam @ A_27a
                  @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0f @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1c ) ) ) ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) @ ( inj__ty_2Erealax_2Ereal @ V1c ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__NEG,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( surj__ty_2Erealax_2Ereal
              @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
                @ ( lam @ A_27a
                  @ ^ [V2x: $i] : ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ V0f @ V2x ) ) ) ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SUB,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
               => ( ( surj__ty_2Erealax_2Ereal
                    @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s )
                      @ ( lam @ A_27a
                        @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__LE,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__LT,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) )
                  & ? [V4x: $i] :
                      ( ( mem @ V4x @ A_27a )
                      & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) )
                      & ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ V0f @ V4x ) ) @ ( ap @ V1g @ V4x ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__LT__ALL,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ( V2s
                   != ( c_2Epred__set_2EEMPTY @ A_27a ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__POS__LT,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
              & ! [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                   => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V0f @ V2x ) ) ) ) )
              & ? [V3x: $i] :
                  ( ( mem @ V3x @ A_27a )
                  & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
                  & ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V0f @ V3x ) ) ) ) )
           => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__POS__LT__ALL,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
              & ( V0s
               != ( c_2Epred__set_2EEMPTY @ A_27a ) )
              & ! [V2i: $i] :
                  ( ( mem @ V2i @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2i ) @ V0s ) )
                   => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V1f @ V2i ) ) ) ) ) )
           => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ V1f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__EQ,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                     => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ V3x ) )
                        = ( surj__ty_2Erealax_2Ereal @ ( ap @ V1g @ V3x ) ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__ABS,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
           => ( p
              @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) )
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
                  @ ( lam @ A_27a
                    @ ^ [V2x: $i] : ( ap @ c_2Ereal_2Eabs @ ( ap @ V0f @ V2x ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__ABS__LE,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ V0f @ V3x ) ) ) @ ( ap @ V1g @ V3x ) ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__CONST,axiom,
    ! [A_27a: del,V0c: tp__ty_2Erealax_2Ereal,V1s: $i] :
      ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
       => ( ( surj__ty_2Erealax_2Ereal
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
              @ ( lam @ A_27a
                @ ^ [V2n: $i] : ( inj__ty_2Erealax_2Ereal @ V0c ) ) ) )
          = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0c ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__POS__LE,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ! [V2x: $i] :
                ( ( mem @ V2x @ A_27a )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V0f @ V2x ) ) ) ) )
           => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__POS__BOUND,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1b: tp__ty_2Erealax_2Ereal,V2s: $i] :
          ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
              & ! [V3x: $i] :
                  ( ( mem @ V3x @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                   => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V0f @ V3x ) ) ) ) )
              & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) ) )
           => ! [V4x: $i] :
                ( ( mem @ V4x @ A_27a )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ V0f @ V4x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1b ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__POS__EQ__0,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
              & ! [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
                   => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V0f @ V2x ) ) ) ) )
              & ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) )
                = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
           => ! [V3x: $i] :
                ( ( mem @ V3x @ A_27a )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
                 => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ V3x ) )
                    = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__ZERO__EXISTS,axiom,
    ! [A_27a: del,V0u: $i] :
      ( ( mem @ V0u @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
              & ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0u ) )
                = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
           => ( ! [V2i: $i] :
                  ( ( mem @ V2i @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2i ) @ V1s ) )
                   => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0u @ V2i ) )
                      = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) )
              | ? [V3j: $i] :
                  ( ( mem @ V3j @ A_27a )
                  & ? [V4k: $i] :
                      ( ( mem @ V4k @ A_27a )
                      & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3j ) @ V1s ) )
                      & ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ V0u @ V3j ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4k ) @ V1s ) )
                      & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__gt @ ( ap @ V0u @ V4k ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__DELETE,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2a: $i] :
              ( ( mem @ V2a @ A_27a )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2a ) @ V1s ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V2a ) ) @ V0f ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) @ ( ap @ V0f @ V2a ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__DELETE__CASES,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2a: $i] :
              ( ( mem @ V2a @ A_27a )
             => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V2a ) ) @ V0f ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2a ) @ V1s ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) @ ( ap @ V0f @ V2a ) ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SING,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ V1x ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__DELTA,axiom,
    ! [A_27a: del,V0b: tp__ty_2Erealax_2Ereal,V1s: $i] :
      ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
     => ! [V2a: $i] :
          ( ( mem @ V2a @ A_27a )
         => ( ( surj__ty_2Erealax_2Ereal
              @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
                @ ( lam @ A_27a
                  @ ^ [V3x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V2a ) ) @ ( inj__ty_2Erealax_2Ereal @ V0b ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2a ) @ V1s ) ) @ ( inj__ty_2Erealax_2Ereal @ V0b ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SWAP,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) ) )
               => ( ( surj__ty_2Erealax_2Ereal
                    @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
                      @ ( lam @ A_27a
                        @ ^ [V3i: $i] : ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ V2t ) @ ( ap @ V0f @ V3i ) ) ) ) )
                  = ( surj__ty_2Erealax_2Ereal
                    @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ V2t )
                      @ ( lam @ A_27b
                        @ ^ [V4j: $i] :
                            ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
                            @ ( lam @ A_27a
                              @ ^ [V5i: $i] : ( ap @ ( ap @ V0f @ V5i ) @ V4j ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__IMAGE,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) )
         => ! [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 ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) ) @ V1g ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ty_2Erealax_2Ereal @ A_27b ) @ V1g ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SUPERSET,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1u: $i] :
          ( ( mem @ V1u @ ( arr @ A_27a @ bool ) )
         => ! [V2v: $i] :
              ( ( mem @ V2v @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1u ) @ V2v ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2v ) )
                          & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1u ) ) )
                       => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ V3x ) )
                          = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2v ) @ V0f ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1u ) @ V0f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__UNION__RZERO,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1u: $i] :
          ( ( mem @ V1u @ ( arr @ A_27a @ bool ) )
         => ! [V2v: $i] :
              ( ( mem @ V2v @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1u ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2v ) )
                          & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1u ) ) )
                       => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ V3x ) )
                          = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1u ) @ V2v ) ) @ V0f ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1u ) @ V0f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__UNION__LZERO,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1u: $i] :
          ( ( mem @ V1u @ ( arr @ A_27a @ bool ) )
         => ! [V2v: $i] :
              ( ( mem @ V2v @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2v ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1u ) )
                          & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2v ) ) )
                       => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ V3x ) )
                          = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1u ) @ V2v ) ) @ V0f ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2v ) @ V0f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__RESTRICT,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
           => ( ( surj__ty_2Erealax_2Ereal
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
                  @ ( lam @ A_27a
                    @ ^ [V2x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) ) @ ( ap @ V0f @ V2x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) )
              = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__BOUND,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2b: tp__ty_2Erealax_2Ereal] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ V1f @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ V1f ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__BOUND__GEN,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2b: tp__ty_2Erealax_2Ereal] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ( V0s
                 != ( c_2Epred__set_2EEMPTY @ A_27a ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ V1f @ V3x ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ V1f ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__ABS__BOUND,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2b: tp__ty_2Erealax_2Ereal] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ V1f @ V3x ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ V1f ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__BOUND__LT,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2b: tp__ty_2Erealax_2Ereal] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ V1f @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) )
                & ? [V4x: $i] :
                    ( ( mem @ V4x @ A_27a )
                    & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V0s ) )
                    & ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ V1f @ V4x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ V1f ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__BOUND__LT__ALL,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2b: tp__ty_2Erealax_2Ereal] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ( V0s
                 != ( c_2Epred__set_2EEMPTY @ A_27a ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ V1f @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ V1f ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__BOUND__LT__GEN,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2b: tp__ty_2Erealax_2Ereal] :
              ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                & ( V0s
                 != ( c_2Epred__set_2EEMPTY @ A_27a ) )
                & ! [V3x: $i] :
                    ( ( mem @ V3x @ A_27a )
                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
                     => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ V1f @ V3x ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ V1f ) ) @ ( inj__ty_2Erealax_2Ereal @ V2b ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__UNION__EQ,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
             => ! [V3u: $i] :
                  ( ( mem @ V3u @ ( arr @ A_27a @ bool ) )
                 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3u ) )
                      & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V2t )
                        = ( c_2Epred__set_2EEMPTY @ A_27a ) )
                      & ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t )
                        = V3u ) )
                   => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2t ) @ V0f ) ) )
                      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V3u ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__EQ__SUPERSET,axiom,
    ! [A_27a: del,V0g: $i] :
      ( ( mem @ V0g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
                 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3t ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V3t ) @ V2s ) )
                      & ! [V4x: $i] :
                          ( ( mem @ V4x @ A_27a )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V3t ) )
                           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V1f @ V4x ) )
                              = ( surj__ty_2Erealax_2Ereal @ ( ap @ V0g @ V4x ) ) ) ) )
                      & ! [V5x: $i] :
                          ( ( mem @ V5x @ A_27a )
                         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V2s ) )
                              & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V3t ) ) )
                           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V1f @ V5x ) )
                              = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) )
                   => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1f ) )
                      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V3t ) @ V0g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__RESTRICT__SET,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
             => ( ( surj__ty_2Erealax_2Ereal
                  @ ( ap
                    @ ( ap @ ( c_2Eiterate_2ESum @ A_27a )
                      @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                        @ ( lam @ A_27a
                          @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) ) @ ( ap @ V0P @ V3x ) ) ) ) ) )
                    @ V2f ) )
                = ( surj__ty_2Erealax_2Ereal
                  @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
                    @ ( lam @ A_27a
                      @ ^ [V4x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ V0P @ V4x ) ) @ ( ap @ V2f @ V4x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SUM__RESTRICT,axiom,
    ! [A_27a: del,A_27b: del,V0R: $i] :
      ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
                 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                      & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V3t ) ) )
                   => ( ( surj__ty_2Erealax_2Ereal
                        @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s )
                          @ ( lam @ A_27a
                            @ ^ [V4x: $i] :
                                ( ap
                                @ ( ap @ ( c_2Eiterate_2ESum @ A_27b )
                                  @ ( 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 @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V5y ) @ V3t ) ) @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) ) ) ) ) )
                                @ ( lam @ A_27b
                                  @ ^ [V6y: $i] : ( ap @ ( ap @ V1f @ V4x ) @ V6y ) ) ) ) ) )
                      = ( surj__ty_2Erealax_2Ereal
                        @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ V3t )
                          @ ( lam @ A_27b
                            @ ^ [V7y: $i] :
                                ( ap
                                @ ( ap @ ( c_2Eiterate_2ESum @ A_27a )
                                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                    @ ( lam @ A_27a
                                      @ ^ [V8x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V8x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V8x ) @ V2s ) ) @ ( ap @ ( ap @ V0R @ V8x ) @ V7y ) ) ) ) ) )
                                @ ( lam @ A_27a
                                  @ ^ [V9x: $i] : ( ap @ ( ap @ V1f @ V9x ) @ V7y ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ECARD__EQ__SUM,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
       => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) )
          = ( surj__ty_2Erealax_2Ereal
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s )
              @ ( lam @ A_27a
                @ ^ [V1x: $i] : ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__MULTICOUNT__GEN,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 ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
             => ! [V3k: $i] :
                  ( ( mem @ V3k @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
                 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                      & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) )
                      & ! [V4j: $i] :
                          ( ( mem @ V4j @ A_27b )
                         => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4j ) @ V2t ) )
                           => ( ( surj__ty_2Enum_2Enum
                                @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a )
                                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                    @ ( lam @ A_27a
                                      @ ^ [V5i: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V5i ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5i ) @ V1s ) ) @ ( ap @ ( ap @ V0R @ V5i ) @ V4j ) ) ) ) ) ) )
                              = ( surj__ty_2Enum_2Enum @ ( ap @ V3k @ V4j ) ) ) ) ) )
                   => ( ( surj__ty_2Erealax_2Ereal
                        @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
                          @ ( lam @ A_27a
                            @ ^ [V6i: $i] :
                                ( ap @ c_2Ereal_2Ereal__of__num
                                @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b )
                                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27b )
                                    @ ( lam @ A_27b
                                      @ ^ [V7j: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ V7j ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V7j ) @ V2t ) ) @ ( ap @ ( ap @ V0R @ V6i ) @ V7j ) ) ) ) ) ) ) ) ) )
                      = ( surj__ty_2Erealax_2Ereal
                        @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ V2t )
                          @ ( lam @ A_27b
                            @ ^ [V8i: $i] : ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ V3k @ V8i ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__MULTICOUNT,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 ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
             => ! [V3k: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                    & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) )
                    & ! [V4j: $i] :
                        ( ( mem @ V4j @ A_27b )
                       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4j ) @ V2t ) )
                         => ( ( surj__ty_2Enum_2Enum
                              @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a )
                                @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                  @ ( lam @ A_27a
                                    @ ^ [V5i: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V5i ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5i ) @ V1s ) ) @ ( ap @ ( ap @ V0R @ V5i ) @ V4j ) ) ) ) ) ) )
                            = V3k ) ) ) )
                 => ( ( surj__ty_2Erealax_2Ereal
                      @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
                        @ ( lam @ A_27a
                          @ ^ [V6i: $i] :
                              ( ap @ c_2Ereal_2Ereal__of__num
                              @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b )
                                @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27b )
                                  @ ( lam @ A_27b
                                    @ ^ [V7j: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ V7j ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V7j ) @ V2t ) ) @ ( ap @ ( ap @ V0R @ V6i ) @ V7j ) ) ) ) ) ) ) ) ) )
                    = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3k ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V2t ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__IMAGE__GEN,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) )
                  = ( surj__ty_2Erealax_2Ereal
                    @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) )
                      @ ( lam @ A_27b
                        @ ^ [V3y: $i] :
                            ( ap
                            @ ( ap @ ( c_2Eiterate_2ESum @ 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_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V4x ) ) @ V3y ) ) ) ) ) )
                            @ V1g ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__GROUP,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
                 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                      & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) ) @ V3t ) ) )
                   => ( ( surj__ty_2Erealax_2Ereal
                        @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ V3t )
                          @ ( lam @ A_27b
                            @ ^ [V4y: $i] :
                                ( ap
                                @ ( ap @ ( c_2Eiterate_2ESum @ 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_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V5x ) ) @ V4y ) ) ) ) ) )
                                @ V1g ) ) ) )
                      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__OF__NUM__SUM,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ A_27a ) @ V1s ) @ V0f ) ) )
              = ( surj__ty_2Erealax_2Ereal
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s )
                  @ ( lam @ A_27a
                    @ ^ [V2x: $i] : ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ V0f @ V2x ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SUBSET,axiom,
    ! [A_27a: del,V0u: $i] :
      ( ( mem @ V0u @ ( arr @ A_27a @ bool ) )
     => ! [V1v: $i] :
          ( ( mem @ V1v @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0u ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1v ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0u ) @ V1v ) ) )
                       => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ V2f @ V3x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) )
                  & ! [V4x: $i] :
                      ( ( mem @ V4x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1v ) @ V0u ) ) )
                       => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V2f @ V4x ) ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0u ) @ V2f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1v ) @ V2f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SUBSET__SIMPLE,axiom,
    ! [A_27a: del,V0u: $i] :
      ( ( mem @ V0u @ ( arr @ A_27a @ bool ) )
     => ! [V1v: $i] :
          ( ( mem @ V1v @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1v ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0u ) @ V1v ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1v ) @ V0u ) ) )
                       => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V2f @ V3x ) ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0u ) @ V2f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1v ) @ V2f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__IMAGE__NONZERO,axiom,
    ! [A_27a: del,A_27b: del,V0d: $i] :
      ( ( mem @ V0d @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) )
     => ! [V1i: $i] :
          ( ( mem @ V1i @ ( arr @ A_27a @ A_27b ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ! [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 ) )
                              & ( V3x != V4y )
                              & ( ( ap @ V1i @ V3x )
                                = ( ap @ V1i @ V4y ) ) )
                           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0d @ ( ap @ V1i @ V3x ) ) )
                              = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V1i ) @ V2s ) ) @ V0d ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ty_2Erealax_2Ereal @ A_27b ) @ V0d ) @ V1i ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__BIJECTION,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1p: $i] :
          ( ( mem @ V1p @ ( arr @ A_27a @ A_27a ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V1p @ V3x ) ) @ V2s ) ) ) )
                  & ! [V4y: $i] :
                      ( ( mem @ V4y @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V2s ) )
                       => ( 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 ) @ V2s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V1p @ V5x ) ) @ V4y ) ) ) ) ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ty_2Erealax_2Ereal @ A_27a ) @ V0f ) @ V1p ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SUM__PRODUCT,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 ) ) )
         => ! [V2x: $i] :
              ( ( mem @ V2x @ ( arr @ A_27a @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                  & ! [V3i: $i] :
                      ( ( mem @ V3i @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3i ) @ V0s ) )
                       => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ V1t @ V3i ) ) ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal
                    @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s )
                      @ ( lam @ A_27a
                        @ ^ [V4i: $i] : ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ ( ap @ V1t @ V4i ) ) @ ( ap @ V2x @ V4i ) ) ) ) )
                  = ( surj__ty_2Erealax_2Ereal
                    @ ( ap
                      @ ( ap @ ( c_2Eiterate_2ESum @ ( 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
                              @ ^ [V5i: $i] :
                                  ( lam @ A_27b
                                  @ ^ [V6j: $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 ) @ V5i ) @ V6j ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5i ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V6j ) @ ( ap @ V1t @ V5i ) ) ) ) ) ) ) ) )
                      @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ty_2Erealax_2Ereal )
                        @ ( lam @ A_27a
                          @ ^ [V7i: $i] :
                              ( lam @ A_27b
                              @ ^ [V8j: $i] : ( ap @ ( ap @ V2x @ V7i ) @ V8j ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__EQ__GENERAL,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 @ ty_2Erealax_2Ereal ) )
             => ! [V3g: $i] :
                  ( ( mem @ V3g @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) )
                 => ! [V4h: $i] :
                      ( ( mem @ V4h @ ( arr @ A_27a @ A_27b ) )
                     => ( ( ! [V5y: $i] :
                              ( ( mem @ V5y @ A_27b )
                             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V5y ) @ V1t ) )
                               => ( p
                                  @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
                                    @ ( lam @ A_27a
                                      @ ^ [V6x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V4h @ V6x ) ) @ V5y ) ) ) ) ) ) )
                          & ! [V7x: $i] :
                              ( ( mem @ V7x @ A_27a )
                             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7x ) @ V0s ) )
                               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V4h @ V7x ) ) @ V1t ) )
                                  & ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V3g @ ( ap @ V4h @ V7x ) ) )
                                    = ( surj__ty_2Erealax_2Ereal @ ( ap @ V2f @ V7x ) ) ) ) ) ) )
                       => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ V2f ) )
                          = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ V1t ) @ V3g ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__EQ__GENERAL__INVERSES,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 @ ty_2Erealax_2Ereal ) )
             => ! [V3g: $i] :
                  ( ( mem @ V3g @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) )
                 => ! [V4h: $i] :
                      ( ( mem @ V4h @ ( arr @ A_27a @ A_27b ) )
                     => ! [V5k: $i] :
                          ( ( mem @ V5k @ ( arr @ A_27b @ A_27a ) )
                         => ( ( ! [V6y: $i] :
                                  ( ( mem @ V6y @ A_27b )
                                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V6y ) @ V1t ) )
                                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V5k @ V6y ) ) @ V0s ) )
                                      & ( ( ap @ V4h @ ( ap @ V5k @ V6y ) )
                                        = V6y ) ) ) )
                              & ! [V7x: $i] :
                                  ( ( mem @ V7x @ A_27a )
                                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7x ) @ V0s ) )
                                   => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V4h @ V7x ) ) @ V1t ) )
                                      & ( ( ap @ V5k @ ( ap @ V4h @ V7x ) )
                                        = V7x )
                                      & ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V3g @ ( ap @ V4h @ V7x ) ) )
                                        = ( surj__ty_2Erealax_2Ereal @ ( ap @ V2f @ V7x ) ) ) ) ) ) )
                           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ V2f ) )
                              = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ V1t ) @ V3g ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__INJECTION,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1p: $i] :
          ( ( mem @ V1p @ ( arr @ A_27a @ A_27a ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V1p @ V3x ) ) @ V2s ) ) ) )
                  & ! [V4x: $i] :
                      ( ( mem @ V4x @ A_27a )
                     => ! [V5y: $i] :
                          ( ( mem @ V5y @ A_27a )
                         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V2s ) )
                              & ( ( ap @ V1p @ V4x )
                                = ( ap @ V1p @ V5y ) ) )
                           => ( V4x = V5y ) ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ty_2Erealax_2Ereal @ A_27a ) @ V0f ) @ V1p ) ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__UNION__NONZERO,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
                  & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2t ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V2t ) ) )
                       => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ V3x ) )
                          = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t ) ) @ V0f ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V1s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2t ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__BIGUNION__NONZERO,axiom,
    ! [A_27a: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1s: $i] :
          ( ( mem @ V1s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( arr @ A_27a @ bool ) ) @ V1s ) )
              & ! [V2t: $i] :
                  ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2t ) @ V1s ) )
                   => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2t ) ) ) )
              & ! [V3t1: $i] :
                  ( ( mem @ V3t1 @ ( arr @ A_27a @ bool ) )
                 => ! [V4t2: $i] :
                      ( ( mem @ V4t2 @ ( arr @ A_27a @ bool ) )
                     => ! [V5x: $i] :
                          ( ( mem @ V5x @ A_27a )
                         => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V3t1 ) @ V1s ) )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V4t2 ) @ V1s ) )
                              & ( V3t1 != V4t2 )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V3t1 ) )
                              & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V4t2 ) ) )
                           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ V5x ) )
                              = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) )
           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1s ) ) @ V0f ) )
              = ( surj__ty_2Erealax_2Ereal
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ( arr @ A_27a @ bool ) ) @ V1s )
                  @ ( lam @ ( arr @ A_27a @ bool )
                    @ ^ [V6t: $i] : ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V6t ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__CASES,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1P: $i] :
          ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
             => ! [V3g: $i] :
                  ( ( mem @ V3g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
                 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
                   => ( ( surj__ty_2Erealax_2Ereal
                        @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s )
                          @ ( lam @ A_27a
                            @ ^ [V4x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ V1P @ V4x ) ) @ ( ap @ V2f @ V4x ) ) @ ( ap @ V3g @ V4x ) ) ) ) )
                      = ( surj__ty_2Erealax_2Ereal
                        @ ( ap
                          @ ( ap @ c_2Erealax_2Ereal__add
                            @ ( ap
                              @ ( ap @ ( c_2Eiterate_2ESum @ 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 ) @ V0s ) ) @ ( ap @ V1P @ V5x ) ) ) ) ) )
                              @ V2f ) )
                          @ ( ap
                            @ ( ap @ ( c_2Eiterate_2ESum @ A_27a )
                              @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
                                @ ( lam @ A_27a
                                  @ ^ [V6x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V6x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V0s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1P @ V6x ) ) ) ) ) ) )
                            @ V3g ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__CASES__1,axiom,
    ! [A_27a: del,V0y: tp__ty_2Erealax_2Ereal,V1f: $i] :
      ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V2s: $i] :
          ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
         => ! [V3a: $i] :
              ( ( mem @ V3a @ A_27a )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3a ) @ V2s ) ) )
               => ( ( surj__ty_2Erealax_2Ereal
                    @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s )
                      @ ( lam @ A_27a
                        @ ^ [V4x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V4x ) @ V3a ) ) @ ( inj__ty_2Erealax_2Ereal @ V0y ) ) @ ( ap @ V1f @ V4x ) ) ) ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1f ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V0y ) ) @ ( ap @ V1f @ V3a ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__LE__INCLUDED,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ! [V3t: $i] :
                  ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
                 => ! [V4i: $i] :
                      ( ( mem @ V4i @ ( arr @ A_27b @ A_27a ) )
                     => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                          & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V3t ) )
                          & ! [V5y: $i] :
                              ( ( mem @ V5y @ A_27b )
                             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V5y ) @ V3t ) )
                               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V1g @ V5y ) ) ) ) )
                          & ! [V6x: $i] :
                              ( ( mem @ V6x @ A_27a )
                             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V2s ) )
                               => ? [V7y: $i] :
                                    ( ( mem @ V7y @ A_27b )
                                    & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V7y ) @ V3t ) )
                                    & ( ( ap @ V4i @ V7y )
                                      = V6x )
                                    & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ V0f @ V6x ) ) @ ( ap @ V1g @ V7y ) ) ) ) ) ) )
                       => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ V3t ) @ V1g ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__IMAGE__LE,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
                  & ! [V3x: $i] :
                      ( ( mem @ V3x @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                       => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V1g @ ( ap @ V0f @ V3x ) ) ) ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) ) @ V1g ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ty_2Erealax_2Ereal @ A_27b ) @ V1g ) @ V0f ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__CLOSED,axiom,
    ! [A_27a: del,V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V2s: $i] :
              ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
             => ( ( ( p @ ( ap @ V0P @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
                  & ! [V3x: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal] :
                      ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) )
                        & ( p @ ( ap @ V0P @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) )
                     => ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) ) )
                  & ! [V5a: $i] :
                      ( ( mem @ V5a @ A_27a )
                     => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5a ) @ V2s ) )
                       => ( p @ ( ap @ V0P @ ( ap @ V1f @ V5a ) ) ) ) ) )
               => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1f ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__ADD__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
         => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ( surj__ty_2Erealax_2Ereal
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ V0f @ V4i ) ) @ ( ap @ V1g @ V4i ) ) ) ) )
              = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V1g ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SUB__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
         => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ( surj__ty_2Erealax_2Ereal
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0f @ V4i ) ) @ ( ap @ V1g @ V4i ) ) ) ) )
              = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V1g ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__LE__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
         => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ! [V4i: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) )
                    & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
                 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V4i ) ) ) @ ( ap @ V1g @ ( inj__ty_2Enum_2Enum @ V4i ) ) ) ) )
             => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V1g ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__EQ__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
         => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ! [V4i: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) )
                    & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
                 => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V4i ) ) )
                    = ( surj__ty_2Erealax_2Ereal @ ( ap @ V1g @ ( inj__ty_2Enum_2Enum @ V4i ) ) ) ) )
             => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) )
                = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V1g ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__ABS__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( p
          @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) ) )
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3i: $i] : ( ap @ c_2Ereal_2Eabs @ ( ap @ V0f @ V3i ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__CONST__NUMSEG,axiom,
    ! [V0c: tp__ty_2Erealax_2Ereal,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
      ( ( surj__ty_2Erealax_2Ereal
        @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
          @ ( lam @ ty_2Enum_2Enum
            @ ^ [V3n: $i] : ( inj__ty_2Erealax_2Ereal @ V0c ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0c ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__EQ__0__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ! [V3i: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) )
                & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
             => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V3i ) ) )
                = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__TRIV__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__POS__LE__NUMSEG,axiom,
    ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2f: $i] :
      ( ( mem @ V2f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ( ! [V3p: tp__ty_2Enum_2Enum] :
            ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) )
              & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
           => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V2f @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) ) )
       => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2f ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__POS__EQ__0__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( ! [V3p: tp__ty_2Enum_2Enum] :
                ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) )
                  & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3p ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
               => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) ) )
            & ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
              = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
         => ! [V4p: tp__ty_2Enum_2Enum] :
              ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V4p ) ) )
                & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4p ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
             => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V4p ) ) )
                = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SING__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1n: tp__ty_2Enum_2Enum] :
          ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V0f ) )
          = ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__CLAUSES__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ( ! [V1m: tp__ty_2Enum_2Enum] :
            ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
        & ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
            ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) ) @ ( ap @ V0f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__SWAP__NUMSEG,axiom,
    ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum,V3d: tp__ty_2Enum_2Enum,V4f: $i] :
      ( ( mem @ V4f @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) ) )
     => ( ( surj__ty_2Erealax_2Ereal
          @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
            @ ( lam @ ty_2Enum_2Enum
              @ ^ [V5i: $i] : ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2c ) ) @ ( inj__ty_2Enum_2Enum @ V3d ) ) ) @ ( ap @ V4f @ V5i ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal
          @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2c ) ) @ ( inj__ty_2Enum_2Enum @ V3d ) ) )
            @ ( lam @ ty_2Enum_2Enum
              @ ^ [V6j: $i] :
                  ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V7i: $i] : ( ap @ ( ap @ V4f @ V7i ) @ V6j ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__ADD__SPLIT,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3p: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__OFFSET,axiom,
    ! [V0p: tp__ty_2Enum_2Enum,V1f: $i] :
      ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
          ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) ) @ V1f ) )
          = ( surj__ty_2Erealax_2Ereal
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V4i: $i] : ( ap @ V1f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V4i ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__OFFSET__0,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal
              @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V3i: $i] : ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3i ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__CLAUSES__LEFT,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__CLAUSES__RIGHT,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,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 ) ) )
            & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V0f ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__PAIR,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V0f ) )
          = ( surj__ty_2Erealax_2Ereal
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V3i ) ) ) @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V3i ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__OF__NUM__SUM__NUMSEG,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ ( ap @ ( c_2Eiterate_2Ensum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) ) )
          = ( surj__ty_2Erealax_2Ereal
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3i: $i] : ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ V0f @ V3i ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__PARTIAL__SUC,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
         => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ( surj__ty_2Erealax_2Ereal
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4k: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0f @ V4k ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V1g @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V4k ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ V1g @ V4k ) ) ) ) ) )
              = ( surj__ty_2Erealax_2Ereal
                @ ( ap
                  @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                    @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ V1g @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ V1g @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) )
                      @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V5k: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V1g @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V5k ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V5k ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ V0f @ V5k ) ) ) ) ) ) )
                  @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__PARTIAL__PRE,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
         => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
              ( ( surj__ty_2Erealax_2Ereal
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4k: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0f @ V4k ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V1g @ V4k ) ) @ ( ap @ V1g @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V4k ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
              = ( surj__ty_2Erealax_2Ereal
                @ ( ap
                  @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                    @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ V1g @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ V1g @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
                      @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V5k: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V1g @ V5k ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V5k ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ V0f @ V5k ) ) ) ) ) ) )
                  @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__DIFFS,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( surj__ty_2Erealax_2Ereal
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3k: $i] : ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0f @ V3k ) ) @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3k ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
          = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__DIFFS__ALT,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
          ( ( surj__ty_2Erealax_2Ereal
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3k: $i] : ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3k ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ V0f @ V3k ) ) ) ) )
          = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__COMBINE__R,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3p: tp__ty_2Enum_2Enum] :
          ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
            & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) @ V0f ) ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) @ V0f ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ESUM__COMBINE__L,axiom,
    ! [V0f: $i] :
      ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3p: 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 ) ) )
            & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
            & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3p ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) @ V0f ) ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) @ V0f ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2ETH,axiom,
    ! [A_27a: del,A_27b: del] :
      ( ! [V0f: $i] :
          ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
         => ! [V1g: $i] :
              ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
             => ! [V2s: $i] :
                  ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
                 => ( ! [V3x: $i] :
                        ( ( mem @ V3x @ A_27a )
                       => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
                         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0f @ V3x ) )
                            = ( surj__ty_2Erealax_2Ereal @ ( ap @ V1g @ V3x ) ) ) ) )
                   => ( ( surj__ty_2Erealax_2Ereal
                        @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s )
                          @ ( lam @ A_27a
                            @ ^ [V4i: $i] : ( ap @ V0f @ V4i ) ) ) )
                      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V2s ) @ V1g ) ) ) ) ) ) )
      & ! [V5f: $i] :
          ( ( mem @ V5f @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
         => ! [V6g: $i] :
              ( ( mem @ V6g @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
             => ! [V7a: tp__ty_2Enum_2Enum,V8b: tp__ty_2Enum_2Enum] :
                  ( ! [V9i: tp__ty_2Enum_2Enum] :
                      ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V7a ) ) @ ( inj__ty_2Enum_2Enum @ V9i ) ) )
                        & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V9i ) ) @ ( inj__ty_2Enum_2Enum @ V8b ) ) ) )
                     => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V5f @ ( inj__ty_2Enum_2Enum @ V9i ) ) )
                        = ( surj__ty_2Erealax_2Ereal @ ( ap @ V6g @ ( inj__ty_2Enum_2Enum @ V9i ) ) ) ) )
                 => ( ( surj__ty_2Erealax_2Ereal
                      @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V7a ) ) @ ( inj__ty_2Enum_2Enum @ V8b ) ) )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V10i: $i] : ( ap @ V5f @ V10i ) ) ) )
                    = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ V7a ) ) @ ( inj__ty_2Enum_2Enum @ V8b ) ) ) @ V6g ) ) ) ) ) )
      & ! [V11f: $i] :
          ( ( mem @ V11f @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) )
         => ! [V12g: $i] :
              ( ( mem @ V12g @ ( arr @ A_27b @ ty_2Erealax_2Ereal ) )
             => ! [V13p: $i] :
                  ( ( mem @ V13p @ ( arr @ A_27b @ bool ) )
                 => ( ! [V14x: $i] :
                        ( ( mem @ V14x @ A_27b )
                       => ( ( p @ ( ap @ V13p @ V14x ) )
                         => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V11f @ V14x ) )
                            = ( surj__ty_2Erealax_2Ereal @ ( ap @ V12g @ V14x ) ) ) ) )
                   => ( ( surj__ty_2Erealax_2Ereal
                        @ ( ap
                          @ ( ap @ ( c_2Eiterate_2ESum @ A_27b )
                            @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27b )
                              @ ( lam @ A_27b
                                @ ^ [V15y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ V15y ) @ ( ap @ V13p @ V15y ) ) ) ) )
                          @ ( lam @ A_27b
                            @ ^ [V16i: $i] : ( ap @ V11f @ V16i ) ) ) )
                      = ( surj__ty_2Erealax_2Ereal
                        @ ( ap
                          @ ( ap @ ( c_2Eiterate_2ESum @ A_27b )
                            @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27b )
                              @ ( lam @ A_27b
                                @ ^ [V17y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ V17y ) @ ( ap @ V13p @ V17y ) ) ) ) )
                          @ V12g ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUB__POW,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2n: 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 @ V2n ) ) )
     => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
        = ( surj__ty_2Erealax_2Ereal
          @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ V3i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V3i ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUB__POW__R1,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1n: 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 @ V1n ) ) )
     => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal
          @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2i: $i] : ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ V2i ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUB__POW__L1,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1n: 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 @ V1n ) ) )
     => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
        = ( surj__ty_2Erealax_2Ereal
          @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
            @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2i: $i] : ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ V2i ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EFORALL__IN__GSPEC,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,A_27f: del,A_27g: del,V0Q: $i] :
      ( ( mem @ V0Q @ ( arr @ A_27b @ bool ) )
     => ( ! [V1P: $i] :
            ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
           => ! [V2f: $i] :
                ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
               => ( ! [V3z: $i] :
                      ( ( mem @ V3z @ A_27b )
                     => ( ( p
                          @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3z )
                            @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27a )
                              @ ( lam @ A_27a
                                @ ^ [V4x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ ( ap @ V2f @ V4x ) ) @ ( ap @ V1P @ V4x ) ) ) ) ) )
                       => ( p @ ( ap @ V0Q @ V3z ) ) ) )
                <=> ! [V5x: $i] :
                      ( ( mem @ V5x @ A_27a )
                     => ( ( p @ ( ap @ V1P @ V5x ) )
                       => ( p @ ( ap @ V0Q @ ( ap @ V2f @ V5x ) ) ) ) ) ) ) )
        & ! [V6P: $i] :
            ( ( mem @ V6P @ ( arr @ A_27c @ ( arr @ A_27d @ bool ) ) )
           => ! [V7f: $i] :
                ( ( mem @ V7f @ ( arr @ A_27c @ ( arr @ A_27d @ A_27b ) ) )
               => ( ! [V8z: $i] :
                      ( ( mem @ V8z @ A_27b )
                     => ( ( p
                          @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V8z )
                            @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ ( ty_2Epair_2Eprod @ A_27c @ A_27d ) )
                              @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27c @ A_27d @ ( ty_2Epair_2Eprod @ A_27b @ bool ) )
                                @ ( lam @ A_27c
                                  @ ^ [V9x: $i] :
                                      ( lam @ A_27d
                                      @ ^ [V10y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ ( ap @ ( ap @ V7f @ V9x ) @ V10y ) ) @ ( ap @ ( ap @ V6P @ V9x ) @ V10y ) ) ) ) ) ) ) )
                       => ( p @ ( ap @ V0Q @ V8z ) ) ) )
                <=> ! [V11x: $i] :
                      ( ( mem @ V11x @ A_27c )
                     => ! [V12y: $i] :
                          ( ( mem @ V12y @ A_27d )
                         => ( ( p @ ( ap @ ( ap @ V6P @ V11x ) @ V12y ) )
                           => ( p @ ( ap @ V0Q @ ( ap @ ( ap @ V7f @ V11x ) @ V12y ) ) ) ) ) ) ) ) )
        & ! [V13P: $i] :
            ( ( mem @ V13P @ ( arr @ A_27e @ ( arr @ A_27f @ ( arr @ A_27g @ bool ) ) ) )
           => ! [V14f: $i] :
                ( ( mem @ V14f @ ( arr @ A_27e @ ( arr @ A_27f @ ( arr @ A_27g @ A_27b ) ) ) )
               => ( ! [V15z: $i] :
                      ( ( mem @ V15z @ A_27b )
                     => ( ( p
                          @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V15z )
                            @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ ( ty_2Epair_2Eprod @ A_27e @ ( ty_2Epair_2Eprod @ A_27f @ A_27g ) ) )
                              @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27e @ ( ty_2Epair_2Eprod @ A_27f @ A_27g ) @ ( ty_2Epair_2Eprod @ A_27b @ bool ) )
                                @ ( lam @ A_27e
                                  @ ^ [V16w: $i] :
                                      ( ap @ ( c_2Epair_2EUNCURRY @ A_27f @ A_27g @ ( ty_2Epair_2Eprod @ A_27b @ bool ) )
                                      @ ( lam @ A_27f
                                        @ ^ [V17x: $i] :
                                            ( lam @ A_27g
                                            @ ^ [V18y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ ( ap @ ( ap @ ( ap @ V14f @ V16w ) @ V17x ) @ V18y ) ) @ ( ap @ ( ap @ ( ap @ V13P @ V16w ) @ V17x ) @ V18y ) ) ) ) ) ) ) ) ) )
                       => ( p @ ( ap @ V0Q @ V15z ) ) ) )
                <=> ! [V19w: $i] :
                      ( ( mem @ V19w @ A_27e )
                     => ! [V20x: $i] :
                          ( ( mem @ V20x @ A_27f )
                         => ! [V21y: $i] :
                              ( ( mem @ V21y @ A_27g )
                             => ( ( p @ ( ap @ ( ap @ ( ap @ V13P @ V19w ) @ V20x ) @ V21y ) )
                               => ( p @ ( ap @ V0Q @ ( ap @ ( ap @ ( ap @ V14f @ V19w ) @ V20x ) @ V21y ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUB__POLYFUN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3n: 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 @ V3n ) ) )
         => ( ( surj__ty_2Erealax_2Ereal
              @ ( ap
                @ ( ap @ c_2Ereal_2Ereal__sub
                  @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0a @ V4i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ V4i ) ) ) ) )
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V5i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0a @ V5i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ V5i ) ) ) ) ) )
            = ( surj__ty_2Erealax_2Ereal
              @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) )
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V6j: $i] :
                        ( ap
                        @ ( ap @ c_2Erealax_2Ereal__mul
                          @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V6j ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                            @ ( lam @ ty_2Enum_2Enum
                              @ ^ [V7i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0a @ V7i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V7i ) @ V6j ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
                        @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ V6j ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__SUB__POLYFUN__ALT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3n: 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 @ V3n ) ) )
         => ( ( surj__ty_2Erealax_2Ereal
              @ ( ap
                @ ( ap @ c_2Ereal_2Ereal__sub
                  @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0a @ V4i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ V4i ) ) ) ) )
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V5i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0a @ V5i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ V5i ) ) ) ) ) )
            = ( surj__ty_2Erealax_2Ereal
              @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) )
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V6j: $i] :
                        ( ap
                        @ ( ap @ c_2Erealax_2Ereal__mul
                          @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V6j ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
                            @ ( lam @ ty_2Enum_2Enum
                              @ ^ [V7k: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V6j ) @ V7k ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ V7k ) ) ) ) )
                        @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ V6j ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__POLYFUN__ROOTBOUND,axiom,
    ! [V0n: tp__ty_2Enum_2Enum,V1c: $i] :
      ( ( mem @ V1c @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ( ~ ! [V2i: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
             => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V1c @ ( inj__ty_2Enum_2Enum @ V2i ) ) )
                = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
       => ( ( p
            @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
              @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
                @ ( lam @ ty_2Erealax_2Ereal
                  @ ^ [V3x: $i] :
                      ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V3x )
                      @ ( ap
                        @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal )
                          @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
                            @ ( lam @ ty_2Enum_2Enum
                              @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V1c @ V4i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ V3x ) @ V4i ) ) ) ) )
                        @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) )
          & ( p
            @ ( ap
              @ ( ap @ c_2Earithmetic_2E_3C_3D
                @ ( ap @ ( c_2Epred__set_2ECARD @ ty_2Erealax_2Ereal )
                  @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
                    @ ( lam @ ty_2Erealax_2Ereal
                      @ ^ [V5x: $i] :
                          ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V5x )
                          @ ( ap
                            @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal )
                              @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
                                @ ( lam @ ty_2Enum_2Enum
                                  @ ^ [V6i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V1c @ V6i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ V5x ) @ V6i ) ) ) ) )
                            @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) )
              @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__POLYFUN__FINITE__ROOTS,axiom,
    ! [V0n: tp__ty_2Enum_2Enum,V1c: $i] :
      ( ( mem @ V1c @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ( ( p
          @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
            @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V2x: $i] :
                    ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V2x )
                    @ ( ap
                      @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal )
                        @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
                          @ ( lam @ ty_2Enum_2Enum
                            @ ^ [V3i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V1c @ V3i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ V2x ) @ V3i ) ) ) ) )
                      @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) )
      <=> ? [V4i: tp__ty_2Enum_2Enum] :
            ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
            & ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V1c @ ( inj__ty_2Enum_2Enum @ V4i ) ) )
             != ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__POLYFUN__EQ__0,axiom,
    ! [V0n: tp__ty_2Enum_2Enum,V1c: $i] :
      ( ( mem @ V1c @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ( ! [V2x: tp__ty_2Erealax_2Ereal] :
            ( ( surj__ty_2Erealax_2Ereal
              @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V3i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V1c @ V3i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V3i ) ) ) ) )
            = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      <=> ! [V4i: tp__ty_2Enum_2Enum] :
            ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
           => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V1c @ ( inj__ty_2Enum_2Enum @ V4i ) ) )
              = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EREAL__POLYFUN__EQ__CONST,axiom,
    ! [V0n: tp__ty_2Enum_2Enum,V1c: $i] :
      ( ( mem @ V1c @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
     => ! [V2k: tp__ty_2Erealax_2Ereal] :
          ( ! [V3x: tp__ty_2Erealax_2Ereal] :
              ( ( surj__ty_2Erealax_2Ereal
                @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V1c @ V4i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V4i ) ) ) ) )
              = V2k )
        <=> ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V1c @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
              = V2k )
            & ! [V5i: tp__ty_2Enum_2Enum] :
                ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V5i ) ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
               => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V1c @ ( inj__ty_2Enum_2Enum @ V5i ) ) )
                  = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eiterate_2Epolynomial__function,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ( ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V0p ) )
      <=> ? [V1m: tp__ty_2Enum_2Enum,V2c: $i] :
            ( ( mem @ V2c @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) )
            & ! [V3x: tp__ty_2Erealax_2Ereal] :
                ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0p @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) )
                = ( surj__ty_2Erealax_2Ereal
                  @ ( ap @ ( ap @ ( c_2Eiterate_2ESum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eiterate_2E_2E_2E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V2c @ V4i ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V4i ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__CONST,axiom,
    ! [V0c: tp__ty_2Erealax_2Ereal] :
      ( p
      @ ( ap @ c_2Eiterate_2Epolynomial__function
        @ ( lam @ ty_2Erealax_2Ereal
          @ ^ [V1x: $i] : ( inj__ty_2Erealax_2Ereal @ V0c ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__ID,axiom,
    ( p
    @ ( ap @ c_2Eiterate_2Epolynomial__function
      @ ( lam @ ty_2Erealax_2Ereal
        @ ^ [V0x: $i] : V0x ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__ADD,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
         => ( ( ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V0p ) )
              & ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V1q ) ) )
           => ( p
              @ ( ap @ c_2Eiterate_2Epolynomial__function
                @ ( lam @ ty_2Erealax_2Ereal
                  @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ V0p @ V2x ) ) @ ( ap @ V1q @ V2x ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__LMUL,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ! [V1c: tp__ty_2Erealax_2Ereal] :
          ( ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V0p ) )
         => ( p
            @ ( ap @ c_2Eiterate_2Epolynomial__function
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1c ) ) @ ( ap @ V0p @ V2x ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__RMUL,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ! [V1c: tp__ty_2Erealax_2Ereal] :
          ( ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V0p ) )
         => ( p
            @ ( ap @ c_2Eiterate_2Epolynomial__function
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0p @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1c ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__NEG,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ( ( p
          @ ( ap @ c_2Eiterate_2Epolynomial__function
            @ ( lam @ ty_2Erealax_2Ereal
              @ ^ [V1x: $i] : ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ V0p @ V1x ) ) ) ) )
      <=> ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V0p ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__SUB,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
         => ( ( ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V0p ) )
              & ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V1q ) ) )
           => ( p
              @ ( ap @ c_2Eiterate_2Epolynomial__function
                @ ( lam @ ty_2Erealax_2Ereal
                  @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0p @ V2x ) ) @ ( ap @ V1q @ V2x ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__MUL,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
         => ( ( ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V0p ) )
              & ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V1q ) ) )
           => ( p
              @ ( ap @ c_2Eiterate_2Epolynomial__function
                @ ( lam @ ty_2Erealax_2Ereal
                  @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V0p @ V2x ) ) @ ( ap @ V1q @ V2x ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__SUM,axiom,
    ! [A_27a: del,V0s: $i] :
      ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
     => ! [V1p: $i] :
          ( ( mem @ V1p @ ( arr @ ty_2Erealax_2Ereal @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) ) )
         => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
              & ! [V2i: $i] :
                  ( ( mem @ V2i @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2i ) @ V0s ) )
                   => ( p
                      @ ( ap @ c_2Eiterate_2Epolynomial__function
                        @ ( lam @ ty_2Erealax_2Ereal
                          @ ^ [V3x: $i] : ( ap @ ( ap @ V1p @ V3x ) @ V2i ) ) ) ) ) ) )
           => ( p
              @ ( ap @ c_2Eiterate_2Epolynomial__function
                @ ( lam @ ty_2Erealax_2Ereal
                  @ ^ [V4x: $i] : ( ap @ ( ap @ ( c_2Eiterate_2ESum @ A_27a ) @ V0s ) @ ( ap @ V1p @ V4x ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__POW,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ! [V1n: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V0p ) )
         => ( p
            @ ( ap @ c_2Eiterate_2Epolynomial__function
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ V0p @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__INDUCT,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ bool ) )
     => ( ( ( p
            @ ( ap @ V0P
              @ ( lam @ ty_2Erealax_2Ereal
                @ ^ [V1x: $i] : V1x ) ) )
          & ! [V2c: tp__ty_2Erealax_2Ereal] :
              ( p
              @ ( ap @ V0P
                @ ( lam @ ty_2Erealax_2Ereal
                  @ ^ [V3x: $i] : ( inj__ty_2Erealax_2Ereal @ V2c ) ) ) )
          & ! [V4p: $i] :
              ( ( mem @ V4p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
             => ! [V5q: $i] :
                  ( ( mem @ V5q @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
                 => ( ( ( p @ ( ap @ V0P @ V4p ) )
                      & ( p @ ( ap @ V0P @ V5q ) ) )
                   => ( p
                      @ ( ap @ V0P
                        @ ( lam @ ty_2Erealax_2Ereal
                          @ ^ [V6x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ V4p @ V6x ) ) @ ( ap @ V5q @ V6x ) ) ) ) ) ) ) )
          & ! [V7p: $i] :
              ( ( mem @ V7p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
             => ! [V8q: $i] :
                  ( ( mem @ V8q @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
                 => ( ( ( p @ ( ap @ V0P @ V7p ) )
                      & ( p @ ( ap @ V0P @ V8q ) ) )
                   => ( p
                      @ ( ap @ V0P
                        @ ( lam @ ty_2Erealax_2Ereal
                          @ ^ [V9x: $i] : ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ V7p @ V9x ) ) @ ( ap @ V8q @ V9x ) ) ) ) ) ) ) ) )
       => ! [V10p: $i] :
            ( ( mem @ V10p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
           => ( ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V10p ) )
             => ( p @ ( ap @ V0P @ V10p ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__o,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
         => ( ( ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V0p ) )
              & ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V1q ) ) )
           => ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ V0p ) @ V1q ) ) ) ) ) ) ).

thf(conj_thm_2Eiterate_2EPOLYNOMIAL__FUNCTION__FINITE__ROOTS,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ! [V1a: tp__ty_2Erealax_2Ereal] :
          ( ( p @ ( ap @ c_2Eiterate_2Epolynomial__function @ V0p ) )
         => ( ( p
              @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Erealax_2Ereal )
                @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
                  @ ( lam @ ty_2Erealax_2Ereal
                    @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V2x ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal ) @ ( ap @ V0p @ V2x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1a ) ) ) ) ) ) )
          <=> ~ ! [V3x: tp__ty_2Erealax_2Ereal] :
                  ( ( surj__ty_2Erealax_2Ereal @ ( ap @ V0p @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) )
                  = V1a ) ) ) ) ).

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