ITP001 Axioms: ITP095^5.ax


%------------------------------------------------------------------------------
% File     : ITP095^5 : 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    : blast^2.ax [Gau20]
%          : HL4095^5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   26 (   0 unt;   4 typ;   0 def)
%            Number of atoms       : 1345 (   8 equ;   0 cnn)
%            Maximal formula atoms :  135 (  51 avg)
%            Number of connectives : 1749 (   3   ~;   2   |;   7   &;1659   @)
%                                         (  19 <=>;  59  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (  14 avg;1659 nst)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   58 (  57 usr;  57 con; 0-2 aty)
%            Number of variables   :  101 (  24   ^  77   !;   0   ?; 101   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Eblast_2EBCARRY,type,
    c_2Eblast_2EBCARRY: $i ).

thf(mem_c_2Eblast_2EBCARRY,axiom,
    mem @ c_2Eblast_2EBCARRY @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ bool @ bool ) ) ) ) ).

thf(tp_c_2Eblast_2EBSUM,type,
    c_2Eblast_2EBSUM: $i ).

thf(mem_c_2Eblast_2EBSUM,axiom,
    mem @ c_2Eblast_2EBSUM @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ bool @ bool ) ) ) ) ).

thf(tp_c_2Eblast_2Ebcarry,type,
    c_2Eblast_2Ebcarry: $i ).

thf(mem_c_2Eblast_2Ebcarry,axiom,
    mem @ c_2Eblast_2Ebcarry @ ( arr @ bool @ ( arr @ bool @ ( arr @ bool @ bool ) ) ) ).

thf(tp_c_2Eblast_2Ebsum,type,
    c_2Eblast_2Ebsum: $i ).

thf(mem_c_2Eblast_2Ebsum,axiom,
    mem @ c_2Eblast_2Ebsum @ ( arr @ bool @ ( arr @ bool @ ( arr @ bool @ bool ) ) ) ).

thf(ax_thm_2Eblast_2Ebcarry__def,axiom,
    ! [V0x: $i] :
      ( ( mem @ V0x @ bool )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ bool )
         => ! [V2c: $i] :
              ( ( mem @ V2c @ bool )
             => ( ( p @ ( ap @ ( ap @ ( ap @ c_2Eblast_2Ebcarry @ V0x ) @ V1y ) @ V2c ) )
              <=> ( ( ( p @ V0x )
                    & ( p @ V1y ) )
                  | ( ( ( p @ V0x )
                      | ( p @ V1y ) )
                    & ( p @ V2c ) ) ) ) ) ) ) ).

thf(ax_thm_2Eblast_2EBCARRY__def,axiom,
    ( ! [V0x: $i] :
        ( ( mem @ V0x @ ( arr @ ty_2Enum_2Enum @ bool ) )
       => ! [V1y: $i] :
            ( ( mem @ V1y @ ( arr @ ty_2Enum_2Enum @ bool ) )
           => ! [V2c: $i] :
                ( ( mem @ V2c @ bool )
               => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0x ) @ V1y ) @ V2c ) )
                <=> ( p @ V2c ) ) ) ) )
    & ! [V3i: tp__ty_2Enum_2Enum,V4x: $i] :
        ( ( mem @ V4x @ ( arr @ ty_2Enum_2Enum @ bool ) )
       => ! [V5y: $i] :
            ( ( mem @ V5y @ ( arr @ ty_2Enum_2Enum @ bool ) )
           => ! [V6c: $i] :
                ( ( mem @ V6c @ bool )
               => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) @ V4x ) @ V5y ) @ V6c ) )
                <=> ( p @ ( ap @ ( ap @ ( ap @ c_2Eblast_2Ebcarry @ ( ap @ V4x @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) @ ( ap @ V5y @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ V4x ) @ V5y ) @ V6c ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2EBCARRY__def__compute,axiom,
    ( ! [V0x: $i] :
        ( ( mem @ V0x @ ( arr @ ty_2Enum_2Enum @ bool ) )
       => ! [V1y: $i] :
            ( ( mem @ V1y @ ( arr @ ty_2Enum_2Enum @ bool ) )
           => ! [V2c: $i] :
                ( ( mem @ V2c @ bool )
               => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0x ) @ V1y ) @ V2c ) )
                <=> ( p @ V2c ) ) ) ) )
    & ! [V3i: tp__ty_2Enum_2Enum,V4x: $i] :
        ( ( mem @ V4x @ ( arr @ ty_2Enum_2Enum @ bool ) )
       => ! [V5y: $i] :
            ( ( mem @ V5y @ ( arr @ ty_2Enum_2Enum @ bool ) )
           => ! [V6c: $i] :
                ( ( mem @ V6c @ bool )
               => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) ) @ V4x ) @ V5y ) @ V6c ) )
                <=> ( p @ ( ap @ ( ap @ ( ap @ c_2Eblast_2Ebcarry @ ( ap @ V4x @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ V5y @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V4x ) @ V5y ) @ V6c ) ) ) ) ) ) )
    & ! [V7i: tp__ty_2Enum_2Enum,V8x: $i] :
        ( ( mem @ V8x @ ( arr @ ty_2Enum_2Enum @ bool ) )
       => ! [V9y: $i] :
            ( ( mem @ V9y @ ( arr @ ty_2Enum_2Enum @ bool ) )
           => ! [V10c: $i] :
                ( ( mem @ V10c @ bool )
               => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V7i ) ) ) ) @ V8x ) @ V9y ) @ V10c ) )
                <=> ( p @ ( ap @ ( ap @ ( ap @ c_2Eblast_2Ebcarry @ ( ap @ V8x @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V7i ) ) ) ) ) @ ( ap @ V9y @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V7i ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V7i ) ) ) ) @ V8x ) @ V9y ) @ V10c ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Eblast_2Ebsum__def,axiom,
    ! [V0x: $i] :
      ( ( mem @ V0x @ bool )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ bool )
         => ! [V2c: $i] :
              ( ( mem @ V2c @ bool )
             => ( ( p @ ( ap @ ( ap @ ( ap @ c_2Eblast_2Ebsum @ V0x ) @ V1y ) @ V2c ) )
              <=> ( ( ( p @ V0x )
                  <=> ~ ( p @ V1y ) )
                <=> ~ ( p @ V2c ) ) ) ) ) ) ).

thf(ax_thm_2Eblast_2EBSUM__def,axiom,
    ! [V0i: tp__ty_2Enum_2Enum,V1x: $i] :
      ( ( mem @ V1x @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V2y: $i] :
          ( ( mem @ V2y @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V3c: $i] :
              ( ( mem @ V3c @ bool )
             => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBSUM @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ V1x ) @ V2y ) @ V3c ) )
              <=> ( p @ ( ap @ ( ap @ ( ap @ c_2Eblast_2Ebsum @ ( ap @ V1x @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) @ ( ap @ V2y @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ V1x ) @ V2y ) @ V3c ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2EBCARRY__LEM,axiom,
    ! [V0i: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum,V3c: $i] :
      ( ( mem @ V3c @ bool )
     => ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) )
       => ( ( p
            @ ( ap
              @ ( ap
                @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( inj__ty_2Enum_2Enum @ V0i ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Ebit_2EBIT @ V4i ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V5i: $i] : ( ap @ ( ap @ c_2Ebit_2EBIT @ V5i ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) )
              @ V3c ) )
        <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V3c ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2EBCARRY__EQ,axiom,
    ! [V0n: tp__ty_2Enum_2Enum,V1c: $i] :
      ( ( mem @ V1c @ bool )
     => ! [V2x1: $i] :
          ( ( mem @ V2x1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V3x2: $i] :
              ( ( mem @ V3x2 @ ( arr @ ty_2Enum_2Enum @ bool ) )
             => ! [V4y1: $i] :
                  ( ( mem @ V4y1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
                 => ! [V5y2: $i] :
                      ( ( mem @ V5y2 @ ( arr @ ty_2Enum_2Enum @ bool ) )
                     => ( ! [V6i: tp__ty_2Enum_2Enum] :
                            ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V6i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
                           => ( ( ( p @ ( ap @ V2x1 @ ( inj__ty_2Enum_2Enum @ V6i ) ) )
                              <=> ( p @ ( ap @ V3x2 @ ( inj__ty_2Enum_2Enum @ V6i ) ) ) )
                              & ( ( p @ ( ap @ V4y1 @ ( inj__ty_2Enum_2Enum @ V6i ) ) )
                              <=> ( p @ ( ap @ V5y2 @ ( inj__ty_2Enum_2Enum @ V6i ) ) ) ) ) )
                       => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2x1 ) @ V4y1 ) @ V1c ) )
                        <=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V3x2 ) @ V5y2 ) @ V1c ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2EBSUM__EQ,axiom,
    ! [V0n: tp__ty_2Enum_2Enum,V1c: $i] :
      ( ( mem @ V1c @ bool )
     => ! [V2x1: $i] :
          ( ( mem @ V2x1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V3x2: $i] :
              ( ( mem @ V3x2 @ ( arr @ ty_2Enum_2Enum @ bool ) )
             => ! [V4y1: $i] :
                  ( ( mem @ V4y1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
                 => ! [V5y2: $i] :
                      ( ( mem @ V5y2 @ ( arr @ ty_2Enum_2Enum @ bool ) )
                     => ( ! [V6i: tp__ty_2Enum_2Enum] :
                            ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V6i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
                           => ( ( ( p @ ( ap @ V2x1 @ ( inj__ty_2Enum_2Enum @ V6i ) ) )
                              <=> ( p @ ( ap @ V3x2 @ ( inj__ty_2Enum_2Enum @ V6i ) ) ) )
                              & ( ( p @ ( ap @ V4y1 @ ( inj__ty_2Enum_2Enum @ V6i ) ) )
                              <=> ( p @ ( ap @ V5y2 @ ( inj__ty_2Enum_2Enum @ V6i ) ) ) ) ) )
                       => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBSUM @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2x1 ) @ V4y1 ) @ V1c ) )
                        <=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBSUM @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V3x2 ) @ V5y2 ) @ V1c ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2EBSUM__LEM,axiom,
    ! [V0i: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum,V3c: $i] :
      ( ( mem @ V3c @ bool )
     => ( ( p
          @ ( ap
            @ ( ap
              @ ( ap @ ( ap @ c_2Eblast_2EBSUM @ ( inj__ty_2Enum_2Enum @ V0i ) )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Ebit_2EBIT @ V4i ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V5i: $i] : ( ap @ ( ap @ c_2Ebit_2EBIT @ V5i ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) )
            @ V3c ) )
      <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V3c ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2EBITWISE__ADD,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0x ) @ V1y )
            = ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2i: $i] : ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBSUM @ V2i ) @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1y ) ) @ c_2Ebool_2EF ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2EBITWISE__SUB,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y )
            = ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2i: $i] : ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBSUM @ V2i ) @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0x ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ bool @ bool ) @ c_2Ebool_2E_7E ) @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1y ) ) ) @ c_2Ebool_2ET ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2EBITWISE__LO,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0x ) @ V1y ) )
          <=> ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eblast_2EBCARRY @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0x ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ bool @ bool ) @ c_2Ebool_2E_7E ) @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1y ) ) ) @ c_2Ebool_2ET ) ) ) ) ) ).

thf(conj_thm_2Eblast_2EBITWISE__MUL,axiom,
    ! [A_27a: del,V0w: $i] :
      ( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1m: $i] :
          ( ( mem @ V1m @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0w ) @ V1m )
            = ( ap
              @ ( ap
                @ ( ap @ ( c_2Elist_2EFOLDL @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
                  @ ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
                    @ ^ [V2a: $i] :
                        ( lam @ ty_2Enum_2Enum
                        @ ^ [V3j: $i] :
                            ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V2a )
                            @ ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
                              @ ( lam @ ty_2Enum_2Enum
                                @ ^ [V4i: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ V3j ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V3j ) @ V4i ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1m ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V4i ) @ V3j ) ) ) ) ) ) ) ) ) )
                @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
              @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2Eword__lsl__bv__expand,axiom,
    ! [A_27a: del,V0w: $i] :
      ( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1m: $i] :
          ( ( mem @ V1m @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl__bv @ A_27a ) @ V0w ) @ V1m )
            = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a ) @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1m ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) )
              @ ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2k: $i] :
                      ( ap
                      @ ( ap @ c_2Ebool_2E_2F_5C
                        @ ( ap
                          @ ( ap
                            @ ( ap @ ( c_2Elist_2EFOLDL @ ty_2Enum_2Enum @ bool )
                              @ ( lam @ bool
                                @ ^ [V3a: $i] :
                                    ( lam @ ty_2Enum_2Enum
                                    @ ^ [V4j: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V3a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1m ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ V4j ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V4j ) @ V2k ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2k ) @ V4j ) ) ) ) ) ) ) )
                            @ c_2Ebool_2EF )
                          @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
                      @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V1m ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2Eword__lsr__bv__expand,axiom,
    ! [A_27a: del,V0w: $i] :
      ( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1m: $i] :
          ( ( mem @ V1m @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr__bv @ A_27a ) @ V0w ) @ V1m )
            = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a ) @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1m ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) )
              @ ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2k: $i] :
                      ( ap
                      @ ( ap @ c_2Ebool_2E_2F_5C
                        @ ( ap
                          @ ( ap
                            @ ( ap @ ( c_2Elist_2EFOLDL @ ty_2Enum_2Enum @ bool )
                              @ ( lam @ bool
                                @ ^ [V3a: $i] :
                                    ( lam @ ty_2Enum_2Enum
                                    @ ^ [V4j: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V3a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1m ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ V4j ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2k ) @ V4j ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2k ) @ V4j ) ) ) ) ) ) ) )
                            @ c_2Ebool_2EF )
                          @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
                      @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V1m ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2Eword__asr__bv__expand,axiom,
    ! [A_27a: del,V0w: $i] :
      ( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1m: $i] :
          ( ( mem @ V1m @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr__bv @ A_27a ) @ V0w ) @ V1m )
            = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a ) @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
              @ ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2k: $i] :
                      ( ap
                      @ ( ap @ c_2Ebool_2E_5C_2F
                        @ ( ap
                          @ ( ap @ c_2Ebool_2E_2F_5C
                            @ ( ap
                              @ ( ap
                                @ ( ap @ ( c_2Elist_2EFOLDL @ ty_2Enum_2Enum @ bool )
                                  @ ( lam @ bool
                                    @ ^ [V3a: $i] :
                                        ( lam @ ty_2Enum_2Enum
                                        @ ^ [V4j: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V3a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1m ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ V4j ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ V0w ) @ V4j ) ) @ V2k ) ) ) ) ) )
                                @ c_2Ebool_2EF )
                              @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
                          @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V1m ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
                      @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V1m ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2Eword__ror__bv__expand,axiom,
    ! [A_27a: del,V0w: $i] :
      ( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1m: $i] :
          ( ( mem @ V1m @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror__bv @ A_27a ) @ V0w ) @ V1m )
            = ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2k: $i] :
                    ( ap
                    @ ( ap
                      @ ( ap @ ( c_2Elist_2EFOLDL @ ty_2Enum_2Enum @ bool )
                        @ ( lam @ bool
                          @ ^ [V3a: $i] :
                              ( lam @ ty_2Enum_2Enum
                              @ ^ [V4j: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V3a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ V1m ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ V4j ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V4j ) @ V2k ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) )
                      @ c_2Ebool_2EF )
                    @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Eblast_2Eword__rol__bv__expand,axiom,
    ! [A_27a: del,V0w: $i] :
      ( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1m: $i] :
          ( ( mem @ V1m @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__rol__bv @ A_27a ) @ V0w ) @ V1m )
            = ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2k: $i] :
                    ( ap
                    @ ( ap
                      @ ( ap @ ( c_2Elist_2EFOLDL @ ty_2Enum_2Enum @ bool )
                        @ ( lam @ bool
                          @ ^ [V3a: $i] :
                              ( lam @ ty_2Enum_2Enum
                              @ ^ [V4j: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V3a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ V1m ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ V4j ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2k ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ V4j ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) )
                      @ c_2Ebool_2EF )
                    @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) ) ).

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