%------------------------------------------------------------------------------
% File     : ITP133^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 set theory export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : HolSmt^2.ax [Gau20]
%          : HL4133^5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  375 (  45 unt;  11 typ;   0 def)
%            Number of atoms       : 9680 ( 214 equ;   0 cnn)
%            Maximal formula atoms :  129 (  25 avg)
%            Number of connectives : 11778 ( 195   ~; 113   |;  31   &;10807   @)
%                                         ( 261 <=>; 371  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  11 avg;10807 nst)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   91 (  88 usr;  83 con; 0-2 aty)
%            Number of variables   : 1080 (   1   ^1079   !;   0   ?;1080   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2EHolSmt_2Earray__ext,type,
    c_2EHolSmt_2Earray__ext: del > del > $i ).

thf(mem_c_2EHolSmt_2Earray__ext,axiom,
    ! [A_27a: del,A_27b: del] : ( mem @ ( c_2EHolSmt_2Earray__ext @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ A_27a ) ) ) ).

thf(tp_c_2EHolSmt_2Exor,type,
    c_2EHolSmt_2Exor: $i ).

thf(mem_c_2EHolSmt_2Exor,axiom,
    mem @ c_2EHolSmt_2Exor @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).

thf(ax_thm_2EHolSmt_2Exor__def,axiom,
    ! [V0x: $i] :
      ( ( mem @ V0x @ bool )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ bool )
         => ( ( p @ ( ap @ ( ap @ c_2EHolSmt_2Exor @ V0x ) @ V1y ) )
          <=> ~ ( ( p @ V0x )
              <=> ( p @ V1y ) ) ) ) ) ).

thf(ax_thm_2EHolSmt_2Earray__ext__def,axiom,
    ! [A_27a: del,A_27b: del,V0A: $i] :
      ( ( mem @ V0A @ ( arr @ A_27a @ A_27b ) )
     => ! [V1B: $i] :
          ( ( mem @ V1B @ ( arr @ A_27a @ A_27b ) )
         => ( ( ap @ ( ap @ ( c_2EHolSmt_2Earray__ext @ A_27a @ A_27b ) @ V0A ) @ V1B )
            = ( ap @ ( c_2Emin_2E_40 @ A_27a )
              @ ( lam @ A_27a
                @ ^ [V2i: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0A @ V2i ) ) @ ( ap @ V1B @ V2i ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2EALL__DISTINCT__NIL,axiom,
    ! [A_27a: del] :
      ( ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
    <=> $true ) ).

thf(conj_thm_2EHolSmt_2EALL__DISTINCT__CONS,axiom,
    ! [A_27a: del,V0h: $i] :
      ( ( mem @ V0h @ A_27a )
     => ! [V1t: $i] :
          ( ( mem @ V1t @ ( ty_2Elist_2Elist @ A_27a ) )
         => ( ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0h ) @ V1t ) ) )
          <=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0h ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1t ) ) )
              & ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ A_27a ) @ V1t ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2ENOT__MEM__NIL,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
      <=> $true ) ) ).

thf(conj_thm_2EHolSmt_2ENOT__MEM__CONS,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1h: $i] :
          ( ( mem @ V1h @ A_27a )
         => ! [V2t: $i] :
              ( ( mem @ V2t @ ( ty_2Elist_2Elist @ A_27a ) )
             => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1h ) @ V2t ) ) ) )
              <=> ( ( V0x != V1h )
                  & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2t ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2EAND__T,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ( p @ V0p )
          & $true )
      <=> ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2ET__AND,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( $true
                & ( p @ V0p ) )
            <=> ( $true
                & ( p @ V1q ) ) )
           => ( ( p @ V0p )
            <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2EF__OR,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( $false
                | ( p @ V0p ) )
            <=> ( $false
                | ( p @ V1q ) ) )
           => ( ( p @ V0p )
            <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2ECONJ__CONG,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ! [V3s: $i] :
                  ( ( mem @ V3s @ bool )
                 => ( ( ( p @ V0p )
                    <=> ( p @ V1q ) )
                   => ( ( ( p @ V2r )
                      <=> ( p @ V3s ) )
                     => ( ( ( p @ V0p )
                          & ( p @ V2r ) )
                      <=> ( ( p @ V1q )
                          & ( p @ V3s ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2ENOT__NOT__ELIM,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ~ ~ ( p @ V0p )
       => ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2ENOT__FALSE,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( p @ V0p )
       => ( ~ ( p @ V0p )
         => $false ) ) ) ).

thf(conj_thm_2EHolSmt_2ENNF__CONJ,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ! [V3s: $i] :
                  ( ( mem @ V3s @ bool )
                 => ( ( ~ ( p @ V0p )
                    <=> ( p @ V2r ) )
                   => ( ( ~ ( p @ V1q )
                      <=> ( p @ V3s ) )
                     => ( ~ ( ( p @ V0p )
                            & ( p @ V1q ) )
                      <=> ( ( p @ V2r )
                          | ( p @ V3s ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2ENNF__DISJ,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ! [V3s: $i] :
                  ( ( mem @ V3s @ bool )
                 => ( ( ~ ( p @ V0p )
                    <=> ( p @ V2r ) )
                   => ( ( ~ ( p @ V1q )
                      <=> ( p @ V3s ) )
                     => ( ~ ( ( p @ V0p )
                            | ( p @ V1q ) )
                      <=> ( ( p @ V2r )
                          & ( p @ V3s ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2ENNF__NOT__NOT,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
            <=> ( p @ V1q ) )
           => ( ~ ~ ( p @ V0p )
            <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2ENEG__IFF__1__1,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V1q )
            <=> ( p @ V0p ) )
           => ~ ( ( p @ V0p )
              <=> ~ ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2ENEG__IFF__1__2,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ~ ( ( p @ V0p )
              <=> ~ ( p @ V1q ) )
           => ( ( p @ V1q )
            <=> ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2ENEG__IFF__2__1,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
            <=> ~ ( p @ V1q ) )
           => ~ ( ( p @ V0p )
              <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2ENEG__IFF__2__2,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ~ ( ( p @ V0p )
              <=> ( p @ V1q ) )
           => ( ( p @ V0p )
            <=> ~ ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2EDISJ__ELIM__1,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ( ( ( p @ V0p )
                    | ( p @ V1q ) )
                 => ( p @ V2r ) )
               => ( ( p @ V0p )
                 => ( p @ V2r ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2EDISJ__ELIM__2,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ( ( ( p @ V0p )
                    | ( p @ V1q ) )
                 => ( p @ V2r ) )
               => ( ( p @ V1q )
                 => ( p @ V2r ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2EIMP__DISJ__1,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
             => ( p @ V1q ) )
           => ( ~ ( p @ V0p )
              | ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2EIMP__DISJ__2,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
             => ( p @ V1q ) )
           => ( ( p @ V0p )
              | ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2EIMP__FALSE,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ~ ( p @ V0p )
         => $false )
       => ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2EAND__IMP__INTRO__SYM,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ( ( ( p @ V0p )
                    & ( p @ V1q ) )
                 => ( p @ V2r ) )
              <=> ( ( p @ V0p )
                 => ( ( p @ V1q )
                   => ( p @ V2r ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2EVALID__IFF__TRUE,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( p @ V0p )
       => ( ( p @ V0p )
        <=> $true ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed001,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ~ ( ( p @ V0p )
              <=> ( p @ V1q ) )
            | ~ ( p @ V0p )
            | ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed002,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ~ ( ( p @ V0p )
              <=> ( p @ V1q ) )
            | ( p @ V0p )
            | ~ ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed003,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
            <=> ~ ( p @ V1q ) )
            | ~ ( p @ V0p )
            | ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed004,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
            <=> ( p @ V1q ) )
            | ( p @ V0p )
            | ~ ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed005,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
            <=> ( p @ V1q ) )
            | ~ ( p @ V0p )
            | ~ ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed006,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
            <=> ( p @ V1q ) )
            | ( p @ V0p )
            | ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed007,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ~ ( ~ ( p @ V0p )
              <=> ( p @ V1q ) )
            | ( p @ V0p )
            | ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed008,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ~ ( ( p @ V0p )
              <=> ~ ( p @ V1q ) )
            | ( p @ V0p )
            | ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed009,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ~ ( p @ V0p )
            | ( p @ V1q )
            | ~ ( ( p @ V0p )
              <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed010,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( p @ V0p )
            | ~ ( p @ V1q )
            | ~ ( ( p @ V0p )
              <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed011,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( p @ V0p )
            | ( p @ V1q )
            | ~ ( ~ ( p @ V0p )
              <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed012,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( p @ V0p )
            | ( p @ V1q )
            | ~ ( ( p @ V0p )
              <=> ~ ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed013,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
              & ~ ( p @ V1q ) )
            | ( p @ V0p )
            | ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed014,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
              & ( p @ V1q ) )
            | ( p @ V0p )
            | ~ ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed015,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
              & ~ ( p @ V1q ) )
            | ~ ( p @ V0p )
            | ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed016,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
              & ( p @ V1q ) )
            | ~ ( p @ V0p )
            | ~ ( p @ V1q ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed017,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ! [V2x: $i] :
              ( ( mem @ V2x @ A_27a )
             => ( ( p @ V0p )
                | ( V1y
                  = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V2x ) @ V1y ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed018,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ A_27a )
             => ( ~ ( p @ V0p )
                | ( V1x
                  = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V1x ) @ V2y ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed019,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ A_27a )
             => ( ( p @ V0p )
                | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V1x ) @ V2y )
                  = V2y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed020,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ A_27a )
             => ( ~ ( p @ V0p )
                | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V1x ) @ V2y )
                  = V1x ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed021,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ( p @ V0p )
                | ( p @ V1q )
                | ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V2r ) @ V1q ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed022,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ~ ( p @ V0p )
                | ( p @ V1q )
                | ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V1q ) @ V2r ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed023,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V1q ) @ V2r ) )
                | ~ ( p @ V0p )
                | ~ ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed024,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V1q ) @ V2r ) )
                | ( p @ V0p )
                | ~ ( p @ V2r ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed025,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ ( ap @ c_2Ebool_2E_7E @ V1q ) ) @ V2r ) )
                | ~ ( p @ V0p )
                | ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed026,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V1q ) @ ( ap @ c_2Ebool_2E_7E @ V2r ) ) )
                | ( p @ V0p )
                | ( p @ V2r ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed027,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V1q ) @ V2r ) )
                | ~ ( p @ V0p )
                | ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ed028,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V1q ) @ V2r ) )
                | ( p @ V0p )
                | ( p @ V2r ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er001,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ( ( V0x = V1y )
          <=> ( V1y = V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er002,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ( ( V0x = V0x )
      <=> $true ) ) ).

thf(conj_thm_2EHolSmt_2Er003,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ( p @ V0p )
        <=> $true )
      <=> ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2Er004,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( $true
        <=> ( p @ V0p ) )
      <=> ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2Er005,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ( p @ V0p )
        <=> $false )
      <=> ~ ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2Er006,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( $false
        <=> ( p @ V0p ) )
      <=> ~ ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2Er007,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
            <=> ~ ( p @ V1q ) )
          <=> ( ( p @ V0p )
            <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er008,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ~ ( ( p @ V0p )
              <=> ~ ( p @ V1q ) )
          <=> ( ( p @ V0p )
            <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er009,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ~ ( ~ ( p @ V0p )
              <=> ( p @ V1q ) )
          <=> ( ( p @ V0p )
            <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er010,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0x ) @ V1y )
            = V0x ) ) ) ).

thf(conj_thm_2EHolSmt_2Er011,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V0x ) @ V1y )
            = V1y ) ) ) ).

thf(conj_thm_2EHolSmt_2Er012,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V1q ) @ c_2Ebool_2ET ) )
          <=> ( ~ ( p @ V0p )
              | ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er013,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V1q ) @ c_2Ebool_2ET ) )
          <=> ( ( p @ V1q )
              | ~ ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er014,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V1q ) @ ( ap @ c_2Ebool_2E_7E @ V1q ) ) )
          <=> ( ( p @ V0p )
            <=> ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er015,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ V1q ) @ ( ap @ c_2Ebool_2E_7E @ V1q ) ) )
          <=> ( ( p @ V1q )
            <=> ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er016,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ ( ap @ c_2Ebool_2E_7E @ V1q ) ) @ V1q ) )
          <=> ( ( p @ V0p )
            <=> ~ ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er017,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ ( ap @ c_2Ebool_2E_7E @ V1q ) ) @ V1q ) )
          <=> ( ~ ( p @ V1q )
            <=> ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er018,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ A_27a )
             => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ c_2Ebool_2E_7E @ V0p ) ) @ V1x ) @ V2y )
                = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V2y ) @ V1x ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er019,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2x: $i] :
              ( ( mem @ V2x @ A_27a )
             => ! [V3y: $i] :
                  ( ( mem @ V3y @ A_27a )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1q ) @ V2x ) @ V3y ) ) @ V2x )
                    = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V0p ) @ ( ap @ c_2Ebool_2E_7E @ V1q ) ) ) @ V3y ) @ V2x ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er020,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2x: $i] :
              ( ( mem @ V2x @ A_27a )
             => ! [V3y: $i] :
                  ( ( mem @ V3y @ A_27a )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1q ) @ V2x ) @ V3y ) ) @ V2x )
                    = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ V1q ) ) @ V0p ) ) @ V3y ) @ V2x ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er021,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2x: $i] :
              ( ( mem @ V2x @ A_27a )
             => ! [V3y: $i] :
                  ( ( mem @ V3y @ A_27a )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1q ) @ V2x ) @ V3y ) ) @ V3y )
                    = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V0p ) @ V1q ) ) @ V2x ) @ V3y ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er022,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2x: $i] :
              ( ( mem @ V2x @ A_27a )
             => ! [V3y: $i] :
                  ( ( mem @ V3y @ A_27a )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1q ) @ V2x ) @ V3y ) ) @ V3y )
                    = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V1q ) @ V0p ) ) @ V2x ) @ V3y ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er023,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ A_27a )
             => ! [V3z: $i] :
                  ( ( mem @ V3z @ A_27a )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V1x ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V2y ) @ V3z ) )
                    = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V1x ) @ V3z ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er024,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2q: $i] :
              ( ( mem @ V2q @ bool )
             => ! [V3y: $i] :
                  ( ( mem @ V3y @ A_27a )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V1x ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V2q ) @ V1x ) @ V3y ) )
                    = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V0p ) @ V2q ) ) @ V1x ) @ V3y ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er025,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2q: $i] :
              ( ( mem @ V2q @ bool )
             => ! [V3y: $i] :
                  ( ( mem @ V3y @ A_27a )
                 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V1x ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V2q ) @ V1x ) @ V3y ) )
                    = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V2q ) @ V0p ) ) @ V1x ) @ V3y ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er026,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ A_27a )
             => ! [V3z: $i] :
                  ( ( mem @ V3z @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V3z ) ) )
                  <=> ( V1x
                      = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V2y ) @ V3z ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er027,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ A_27a )
             => ! [V3z: $i] :
                  ( ( mem @ V3z @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V2y ) @ V3z ) ) )
                  <=> ( V2y
                      = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V1x ) @ V3z ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er028,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: $i] :
          ( ( mem @ V1x @ A_27a )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ A_27a )
             => ! [V3z: $i] :
                  ( ( mem @ V3z @ A_27a )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0p ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3z ) @ V2y ) ) )
                  <=> ( V2y
                      = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0p ) @ V1x ) @ V3z ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er029,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
             => ( p @ V1q ) )
          <=> ( ( p @ V0p )
              | ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er030,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
             => ( p @ V1q ) )
          <=> ( ( p @ V1q )
              | ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er031,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
             => ( p @ V1q ) )
          <=> ( ~ ( p @ V0p )
              | ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er032,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
             => ( p @ V1q ) )
          <=> ( ( p @ V1q )
              | ~ ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er033,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( $true
         => ( p @ V0p ) )
      <=> ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2Er034,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ( p @ V0p )
         => $true )
      <=> $true ) ) ).

thf(conj_thm_2EHolSmt_2Er035,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( $false
         => ( p @ V0p ) )
      <=> $true ) ) ).

thf(conj_thm_2EHolSmt_2Er036,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ( p @ V0p )
         => ( p @ V0p ) )
      <=> $true ) ) ).

thf(conj_thm_2EHolSmt_2Er037,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ bool )
             => ( ( ( ( p @ V0p )
                  <=> ( p @ V1q ) )
                 => ( p @ V2r ) )
              <=> ( ( p @ V2r )
                  | ( ( p @ V1q )
                  <=> ~ ( p @ V0p ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er038,axiom,
    ( ~ $true
  <=> $false ) ).

thf(conj_thm_2EHolSmt_2Er039,axiom,
    ( ~ $false
  <=> $true ) ).

thf(conj_thm_2EHolSmt_2Er040,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ~ ~ ( p @ V0p )
      <=> ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2Er041,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
              | ( p @ V1q ) )
          <=> ( ( p @ V1q )
              | ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er042,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ( p @ V0p )
          | $true )
      <=> $true ) ) ).

thf(conj_thm_2EHolSmt_2Er043,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ( p @ V0p )
          | ~ ( p @ V0p ) )
      <=> $true ) ) ).

thf(conj_thm_2EHolSmt_2Er044,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ~ ( p @ V0p )
          | ( p @ V0p ) )
      <=> $true ) ) ).

thf(conj_thm_2EHolSmt_2Er045,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( $true
          | ( p @ V0p ) )
      <=> $true ) ) ).

thf(conj_thm_2EHolSmt_2Er046,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ( p @ V0p )
          | $false )
      <=> ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2Er047,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( $false
          | ( p @ V0p ) )
      <=> ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2Er048,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
              & ( p @ V1q ) )
          <=> ( ( p @ V1q )
              & ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er049,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ( p @ V0p )
          & $true )
      <=> ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2Er050,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( $true
          & ( p @ V0p ) )
      <=> ( p @ V0p ) ) ) ).

thf(conj_thm_2EHolSmt_2Er051,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( ( p @ V0p )
          & $false )
      <=> $false ) ) ).

thf(conj_thm_2EHolSmt_2Er052,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ( ( $false
          & ( p @ V0p ) )
      <=> $false ) ) ).

thf(conj_thm_2EHolSmt_2Er053,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
              & ( p @ V1q ) )
          <=> ~ ( ~ ( p @ V0p )
                | ~ ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er054,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
              & ( p @ V1q ) )
          <=> ~ ( ( p @ V0p )
                | ~ ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er055,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
              & ~ ( p @ V1q ) )
          <=> ~ ( ~ ( p @ V0p )
                | ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er056,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
              & ~ ( p @ V1q ) )
          <=> ~ ( ( p @ V0p )
                | ( p @ V1q ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er057,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
              & ( p @ V1q ) )
          <=> ~ ( ~ ( p @ V1q )
                | ~ ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er058,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
              & ( p @ V1q ) )
          <=> ~ ( ~ ( p @ V1q )
                | ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er059,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ( p @ V0p )
              & ~ ( p @ V1q ) )
          <=> ~ ( ( p @ V1q )
                | ~ ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er060,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ bool )
         => ( ( ~ ( p @ V0p )
              & ~ ( p @ V1q ) )
          <=> ~ ( ( p @ V1q )
                | ( p @ V0p ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er061,axiom,
    ! [A_27a: del,A_27b: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1f: $i] :
          ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
         => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V0x ) @ ( ap @ V1f @ V0x ) ) @ V1f )
            = V1f ) ) ) ).

thf(conj_thm_2EHolSmt_2Er062,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ( ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) )
      <=> $false ) ) ).

thf(conj_thm_2EHolSmt_2Er063,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ( ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1y ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) )
          <=> ( V0x != V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er064,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ( ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1y ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) )
          <=> ( V1y != V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er065,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( V0x = V1y )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er066,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( V0x
        = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
        = V1y ) ) ).

thf(conj_thm_2EHolSmt_2Er067,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( V0x
        = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er068,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( V0x
        = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er069,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( V0x
        = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er070,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( V0x
        = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er071,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( V0x
        = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er072,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( V0x
        = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er073,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( V0x
        = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) )
        = V1y ) ) ).

thf(conj_thm_2EHolSmt_2Er074,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) )
    <=> ( V0x = V1y ) ) ).

thf(conj_thm_2EHolSmt_2Er075,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
        = V2z )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er076,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( V1y
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er077,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
        = V2z )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er078,axiom,
    ! [V0a: tp__ty_2Einteger_2Eint,V1x: tp__ty_2Einteger_2Eint,V2v: tp__ty_2Einteger_2Eint,V3y: tp__ty_2Einteger_2Eint,V4w: tp__ty_2Einteger_2Eint,V5z: tp__ty_2Einteger_2Eint] :
      ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1x ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( inj__ty_2Einteger_2Eint @ V2v ) ) @ ( inj__ty_2Einteger_2Eint @ V3y ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( inj__ty_2Einteger_2Eint @ V4w ) ) @ ( inj__ty_2Einteger_2Eint @ V5z ) ) ) ) ) )
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V2v ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3y ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V4w ) ) ) @ ( inj__ty_2Einteger_2Eint @ V5z ) ) ) ) )
        = V0a ) ) ).

thf(conj_thm_2EHolSmt_2Er079,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) )
      = V0x ) ).

thf(conj_thm_2EHolSmt_2Er080,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      = V0x ) ).

thf(conj_thm_2EHolSmt_2Er081,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er082,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er083,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er084,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er085,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er086,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er087,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint,V3u: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( inj__ty_2Einteger_2Eint @ V3u ) ) ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V3u ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er088,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) )
    <=> $true ) ).

thf(conj_thm_2EHolSmt_2Er089,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er090,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er091,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er092,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er093,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er094,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er095,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er096,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__gt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er097,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__gt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er098,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__gt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er099,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__gt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er100,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__gt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er101,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) )
    <=> $true ) ).

thf(conj_thm_2EHolSmt_2Er102,axiom,
    ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
  <=> $true ) ).

thf(conj_thm_2EHolSmt_2Er103,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er104,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er105,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er106,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er107,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er108,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er109,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er110,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er111,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er112,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er113,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er114,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er115,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er116,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er117,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er118,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er119,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er120,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er121,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er122,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint,V3u: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( inj__ty_2Einteger_2Eint @ V3u ) ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V3u ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er123,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint,V3u: tp__ty_2Einteger_2Eint,V4v: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V3u ) ) @ ( inj__ty_2Einteger_2Eint @ V4v ) ) ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V3u ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V4v ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er124,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er125,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2z ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er126,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er127,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      = V0x ) ).

thf(conj_thm_2EHolSmt_2Er128,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er129,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er130,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er131,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er132,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er133,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er134,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er135,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint,V2z: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2z ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er136,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] :
      ( ( ( 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_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er137,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er138,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V0a ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er139,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V0a ) ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er140,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er141,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er142,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal] :
      ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) )
        = V0a ) ) ).

thf(conj_thm_2EHolSmt_2Er143,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal,V5w: tp__ty_2Erealax_2Ereal,V6z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er144,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal,V5w: tp__ty_2Erealax_2Ereal,V6z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er145,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal,V5w: tp__ty_2Erealax_2Ereal,V6z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er146,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal,V5w: tp__ty_2Erealax_2Ereal,V6z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er147,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal,V5w: tp__ty_2Erealax_2Ereal,V6z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er148,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal,V5w: tp__ty_2Erealax_2Ereal,V6z: tp__ty_2Erealax_2Ereal] :
      ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) )
        = V0a ) ) ).

thf(conj_thm_2EHolSmt_2Er149,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal,V5w: tp__ty_2Erealax_2Ereal,V6z: tp__ty_2Erealax_2Ereal] :
      ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) )
        = V0a ) ) ).

thf(conj_thm_2EHolSmt_2Er150,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal,V5w: tp__ty_2Erealax_2Ereal,V6z: tp__ty_2Erealax_2Ereal] :
      ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) )
        = V0a ) ) ).

thf(conj_thm_2EHolSmt_2Er151,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3v: tp__ty_2Erealax_2Ereal,V4y: tp__ty_2Erealax_2Ereal,V5w: tp__ty_2Erealax_2Ereal,V6z: tp__ty_2Erealax_2Ereal] :
      ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3v ) ) @ ( inj__ty_2Erealax_2Ereal @ V4y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V5w ) ) @ ( inj__ty_2Erealax_2Ereal @ V6z ) ) ) ) )
        = V0a ) ) ).

thf(conj_thm_2EHolSmt_2Er152,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er153,axiom,
    ! [V0a: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2x: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal] :
      ( ( V0a
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er154,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4a: tp__ty_2Erealax_2Ereal] :
      ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) )
        = V4a ) ) ).

thf(conj_thm_2EHolSmt_2Er155,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1v: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) )
        = V5a ) ) ).

thf(conj_thm_2EHolSmt_2Er156,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) )
        = V6a ) ) ).

thf(conj_thm_2EHolSmt_2Er157,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) )
        = V6a ) ) ).

thf(conj_thm_2EHolSmt_2Er158,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) )
        = V6a ) ) ).

thf(conj_thm_2EHolSmt_2Er159,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V1y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er160,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V1y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er161,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__gt @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V1y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er162,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V1y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er163,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V2z ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er164,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er165,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er166,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er167,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er168,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er169,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er170,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er171,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er172,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er173,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er174,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er175,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er176,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er177,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er178,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er179,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er180,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er181,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er182,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er183,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1v: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) )
    <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er184,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er185,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er186,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er187,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er188,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er189,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er190,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er191,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er192,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er193,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er194,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er195,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er196,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er197,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er198,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er199,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er200,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal,V6a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V6a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er201,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er202,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4w: tp__ty_2Erealax_2Ereal,V5z: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V4w ) ) @ ( inj__ty_2Erealax_2Ereal @ V5z ) ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er203,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1v: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er204,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1v: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er205,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1v: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er206,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1v: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er207,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1v: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er208,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1v: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er209,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1v: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er210,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1v: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1v ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er211,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal,V3w: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V2y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V3w ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er212,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal,V2v: tp__ty_2Erealax_2Ereal,V3y: tp__ty_2Erealax_2Ereal,V4z: tp__ty_2Erealax_2Ereal,V5a: tp__ty_2Erealax_2Ereal] :
      ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V4z ) ) ) ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) )
    <=> ~ ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2v ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3y ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V4z ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V5a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er213,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
      = V0x ) ).

thf(conj_thm_2EHolSmt_2Er214,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      = V0x ) ).

thf(conj_thm_2EHolSmt_2Er215,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er216,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er217,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er218,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er219,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er220,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er221,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er222,axiom,
    ! [V0u: tp__ty_2Erealax_2Ereal,V1x: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V0u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er223,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      = V0x ) ).

thf(conj_thm_2EHolSmt_2Er224,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er225,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V1y ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er226,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er227,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1u: tp__ty_2Erealax_2Ereal,V2y: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V1u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2y ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er228,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V2z ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er229,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2z: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2z ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V2z ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er230,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2u: tp__ty_2Erealax_2Ereal,V3z: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2u ) ) @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er231,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2u: tp__ty_2Erealax_2Ereal,V3z: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2u ) ) @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er232,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2u: tp__ty_2Erealax_2Ereal,V3z: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V2u ) ) @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ V2u ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er233,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er234,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( 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 ) ) )
      = V0x ) ).

thf(conj_thm_2EHolSmt_2Er235,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0x )
        = V0x ) ) ).

thf(conj_thm_2EHolSmt_2Er236,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 @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V1y ) @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er237,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V0x ) )
        = ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V0x ) ) ) ).

thf(conj_thm_2EHolSmt_2Er238,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1z: $i] :
          ( ( mem @ V1z @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
             => ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0x ) @ V1z )
                  = ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V2y ) @ V0x ) )
              <=> ( V2y = V1z ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er239,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0x: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
     => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
       => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
          = ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er240,axiom,
    ! [A_27a: del,A_27b: del,V0x: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
     => ( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
        = ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er241,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0y: tp__ty_2Enum_2Enum,V1x: $i] :
      ( ( mem @ V1x @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
     => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
       => ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0y ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
           => ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V1x )
                = ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) )
            <=> ( V1x
                = ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er242,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0y: tp__ty_2Enum_2Enum,V1x: $i] :
      ( ( mem @ V1x @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
     => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
       => ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0y ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
           => ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V1x )
                = ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) )
            <=> ( ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0y ) )
                = V1x ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er243,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0y: tp__ty_2Enum_2Enum,V1x: $i] :
      ( ( mem @ V1x @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
     => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
       => ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0y ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
           => ( ( ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V0y ) )
                = ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V1x ) )
            <=> ( V1x
                = ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er244,axiom,
    ! [A_27a: del,A_27b: del,A_27c: del,V0y: tp__ty_2Enum_2Enum,V1x: $i] :
      ( ( mem @ V1x @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
     => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
       => ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0y ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
         => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
           => ( ( ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V0y ) )
                = ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V1x ) )
            <=> ( ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0y ) )
                = V1x ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er245,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__and @ A_27a ) @ V0x ) @ V1y )
            = ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1y ) @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er246,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ! [V2z: $i] :
              ( ( mem @ V2z @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
             => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1y ) @ V2z ) )
                = ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1y ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0x ) @ V2z ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er247,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ! [V2z: $i] :
              ( ( mem @ V2z @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
             => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1y ) @ V2z ) )
                = ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0x ) @ V1y ) ) @ V2z ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er248,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,V1y: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
        = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1y ) ) ) )
    <=> ( ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
          = V0x )
        & ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
          = V1y ) ) ) ).

thf(conj_thm_2EHolSmt_2Er249,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,V1y: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
        = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1y ) ) ) )
    <=> ( ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
          = V1y )
        & ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
          = V0x ) ) ) ).

thf(stp_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
    tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).

thf(stp_inj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
    inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).

thf(stp_surj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
    surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).

thf(stp_inj_surj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
    ! [X: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
      ( ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
      = X ) ).

thf(stp_inj_mem_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
    ! [X: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ).

thf(stp_iso_mem_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
    ! [X: $i] :
      ( ( mem @ X @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) )
     => ( X
        = ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er250,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
      ( ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) )
      = V0x ) ).

thf(conj_thm_2EHolSmt_2Er251,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 @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1y ) @ V0x ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er252,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__mul @ A_27a ) @ V0x ) @ V1y )
            = ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V1y ) @ V0x ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er253,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ ty_2Eone_2Eone @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) )
      = V0x ) ).

thf(conj_thm_2EHolSmt_2Er254,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ! [V2z: $i] :
              ( ( mem @ V2z @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
             => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0x ) @ V1y ) ) @ V2z )
                = ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1y ) @ V2z ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Er255,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0x )
        = V0x ) ) ).

thf(conj_thm_2EHolSmt_2Et001,axiom,
    ! [A_27a: del,A_27b: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
             => ! [V3z: $i] :
                  ( ( mem @ V3z @ A_27b )
                 => ( ( V0x = V1y )
                    | ( ( ap @ V2f @ V0x )
                      = ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1y ) @ V3z ) @ V2f ) @ V0x ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et002,axiom,
    ! [A_27a: del,A_27b: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ! [V2f: $i] :
              ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
             => ! [V3z: $i] :
                  ( ( mem @ V3z @ A_27b )
                 => ( ( V0x = V1y )
                    | ( ( ap @ V2f @ V1y )
                      = ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V0x ) @ V3z ) @ V2f ) @ V1y ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et003,axiom,
    ! [A_27a: del,A_27b: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ! [V2z: $i] :
              ( ( mem @ V2z @ A_27b )
             => ! [V3f: $i] :
                  ( ( mem @ V3f @ ( arr @ A_27a @ A_27b ) )
                 => ( ( V0x = V1y )
                    | ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1y ) @ V2z ) @ V3f ) @ V0x )
                      = ( ap @ V3f @ V0x ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et004,axiom,
    ! [A_27a: del,A_27b: del,V0x: $i] :
      ( ( mem @ V0x @ A_27a )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ A_27a )
         => ! [V2z: $i] :
              ( ( mem @ V2z @ A_27b )
             => ! [V3f: $i] :
                  ( ( mem @ V3f @ ( arr @ A_27a @ A_27b ) )
                 => ( ( V0x = V1y )
                    | ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V0x ) @ V2z ) @ V3f ) @ V1y )
                      = ( ap @ V3f @ V1y ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et005,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
         => ( ( V0f = V1g )
            | ( ( ap @ V0f @ ( ap @ ( ap @ ( c_2EHolSmt_2Earray__ext @ A_27a @ A_27b ) @ V0f ) @ V1g ) )
             != ( ap @ V1g @ ( ap @ ( ap @ ( c_2EHolSmt_2Earray__ext @ A_27a @ A_27b ) @ V0f ) @ V1g ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et006,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( V0x != V1y )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et007,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( V0x != V1y )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et008,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( V0x != V1y )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et009,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( V0x != V1y )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et010,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( V0x = V1y )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et011,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et012,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et013,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et014,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint] :
      ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et015,axiom,
    ! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et016,axiom,
    ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
      ( ( V0x != V1y )
      | ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Erealax_2Ereal__neg @ ( 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 @ V1y ) ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et017,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ( V0x
       != ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0x ) ) ) ).

thf(conj_thm_2EHolSmt_2Et018,axiom,
    ! [A_27a: del,V0x: $i] :
      ( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
         => ! [V2i: tp__ty_2Enum_2Enum] :
              ( ( V0x = V1y )
             => ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0x ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) )
               => ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1y ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et019,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
        = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Eword__1comp @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) ) )
      | ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et020,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
     => ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Eword__1comp @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et021,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
     => ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
        = V0x ) ) ).

thf(conj_thm_2EHolSmt_2Et022,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
     => ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        = V0x ) ) ).

thf(conj_thm_2EHolSmt_2Et023,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
     => ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
        = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Eword__1comp @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et024,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Eword__1comp @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) ) )
      | ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et025,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,V1y: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
        = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ ty_2Eone_2Eone ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1y ) ) ) ) )
      | ~ ( ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
          | ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et026,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
      ( ( ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        = V0x )
      | ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
      | ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
      | ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
      | ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
      | ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
      | ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
      | ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
      | ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et027,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,V1p: $i] :
      ( ( mem @ V1p @ bool )
     => ( ( ( V0x
            = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
        <=> ( p @ V1p ) )
      <=> ( V0x
          = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1p ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et028,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,V1p: $i] :
      ( ( mem @ V1p @ bool )
     => ( ( ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
            = V0x )
        <=> ( p @ V1p ) )
      <=> ( V0x
          = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1p ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et029,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
          ( ( ( p @ V0p )
          <=> ( V1x
              = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
        <=> ( V1x
            = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V0p ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et030,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ bool )
     => ! [V1x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
          ( ( ( p @ V0p )
          <=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
              = V1x ) )
        <=> ( V1x
            = ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V0p ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(stp_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
    tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).

thf(stp_inj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
    inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).

thf(stp_surj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
    surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).

thf(stp_inj_surj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
    ! [X: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
      ( ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
      = X ) ).

thf(stp_inj_mem_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
    ! [X: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ).

thf(stp_iso_mem_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
    ! [X: $i] :
      ( ( mem @ X @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) )
     => ( X
        = ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et031,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
      ( ( ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        = ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2Esw2sw @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) ) ) )
     => ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et032,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
      ( ( ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        = ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2Esw2sw @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) ) ) )
     => ~ ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
        <=> ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et033,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
      ( ( ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        = ( surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2Esw2sw @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) ) ) )
     => ~ ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
        <=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
            & ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et034,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 ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V0x )
              = V1y )
           => ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0x ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
             => ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1y ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Et035,axiom,
    ! [V0x: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
      ( ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
        = V0x )
      | ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ ty_2Eone_2Eone @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x ) ) )
       != ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ep001,axiom,
    ! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ep002,axiom,
    ! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ep003,axiom,
    p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ep004,axiom,
    p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Eone_2Eone ) @ ( c_2Epred__set_2EUNIV @ ty_2Eone_2Eone ) ) ).

thf(conj_thm_2EHolSmt_2Ep005,axiom,
    p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ep006,axiom,
    p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ep007,axiom,
    p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ).

thf(stp_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
    tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).

thf(stp_inj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
    inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).

thf(stp_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
    surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).

thf(stp_inj_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
    ! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
      ( ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
      = X ) ).

thf(stp_inj_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
    ! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ).

thf(stp_iso_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
    ! [X: $i] :
      ( ( mem @ X @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) )
     => ( X
        = ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ep008,axiom,
    p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ).

thf(conj_thm_2EHolSmt_2Ep009,axiom,
    p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) ).

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