ITP001 Axioms: ITP133^7.ax


%------------------------------------------------------------------------------
% File     : ITP133^7 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : HolSmt.ax [Gau19]
%          : HL4133^7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  433 ( 148 unt;  73 typ;   0 def)
%            Number of atoms       :  808 ( 284 equ; 196 cnn)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives : 5100 ( 196   ~; 114   |;  32   &;4497   @)
%                                         ( 193 <=>;  68  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg;4497 nst)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :  123 ( 123   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   70 (  68 usr;   5 con; 0-6 aty)
%            Number of variables   : 1123 (   1   ^1083   !;   1   ?;1123   :)
%                                         (  38  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Ebool_2Eitself,type,
    tyop_2Ebool_2Eitself: $tType > $tType ).

thf(tyop_2Efcp_2Ebit0,type,
    tyop_2Efcp_2Ebit0: $tType > $tType ).

thf(tyop_2Efcp_2Ebit1,type,
    tyop_2Efcp_2Ebit1: $tType > $tType ).

thf(tyop_2Efcp_2Ecart,type,
    tyop_2Efcp_2Ecart: $tType > $tType > $tType ).

thf(tyop_2Einteger_2Eint,type,
    tyop_2Einteger_2Eint: $tType ).

thf(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: $tType > $tType ).

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

thf(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: $tType > $tType > $tType ).

thf(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: $tType ).

thf(tyop_2Eone_2Eone,type,
    tyop_2Eone_2Eone: $tType ).

thf(tyop_2Erealax_2Ereal,type,
    tyop_2Erealax_2Ereal: $tType ).

thf(c_2Ebool_2E_21,type,
    c_2Ebool_2E_21: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Ebool_2E_2F_5C,type,
    c_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(c_2Enum_2E0,type,
    c_2Enum_2E0: tyop_2Enum_2Enum ).

thf(c_2Eprim__rec_2E_3C,type,
    c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2E_3C_3D,type,
    c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Emin_2E_3D,type,
    c_2Emin_2E_3D: 
      !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).

thf(c_2Emin_2E_3D_3D_3E,type,
    c_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(c_2Ebool_2E_3F,type,
    c_2Ebool_2E_3F: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Emin_2E_40,type,
    c_2Emin_2E_40: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).

thf(c_2Elist_2EALL__DISTINCT,type,
    c_2Elist_2EALL__DISTINCT: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).

thf(c_2Earithmetic_2EBIT1,type,
    c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2EBIT2,type,
    c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Ebool_2ECOND,type,
    c_2Ebool_2ECOND: 
      !>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).

thf(c_2Elist_2ECONS,type,
    c_2Elist_2ECONS: 
      !>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Ebool_2EF,type,
    c_2Ebool_2EF: $o ).

thf(c_2Epred__set_2EFINITE,type,
    c_2Epred__set_2EFINITE: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Ebool_2EIN,type,
    c_2Ebool_2EIN: 
      !>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).

thf(c_2Elist_2ELIST__TO__SET,type,
    c_2Elist_2ELIST__TO__SET: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27a > $o ) ).

thf(c_2Elist_2ENIL,type,
    c_2Elist_2ENIL: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).

thf(c_2Earithmetic_2ENUMERAL,type,
    c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Ebool_2ET,type,
    c_2Ebool_2ET: $o ).

thf(c_2Epred__set_2EUNIV,type,
    c_2Epred__set_2EUNIV: 
      !>[A_27a: $tType] : ( A_27a > $o ) ).

thf(c_2Ecombin_2EUPDATE,type,
    c_2Ecombin_2EUPDATE: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( A_27a > A_27b ) > A_27a > A_27b ) ).

thf(c_2Earithmetic_2EZERO,type,
    c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).

thf(c_2Ebool_2E_5C_2F,type,
    c_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(c_2EHolSmt_2Earray__ext,type,
    c_2EHolSmt_2Earray__ext: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27a > A_27b ) > A_27a ) ).

thf(c_2Efcp_2Edimindex,type,
    c_2Efcp_2Edimindex: 
      !>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).

thf(c_2Ewords_2Edimword,type,
    c_2Ewords_2Edimword: 
      !>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).

thf(c_2Efcp_2Efcp__index,type,
    c_2Efcp_2Efcp__index: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) > tyop_2Enum_2Enum > A_27a ) ).

thf(c_2Einteger_2Eint__add,type,
    c_2Einteger_2Eint__add: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__ge,type,
    c_2Einteger_2Eint__ge: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).

thf(c_2Einteger_2Eint__gt,type,
    c_2Einteger_2Eint__gt: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).

thf(c_2Einteger_2Eint__le,type,
    c_2Einteger_2Eint__le: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).

thf(c_2Einteger_2Eint__lt,type,
    c_2Einteger_2Eint__lt: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).

thf(c_2Einteger_2Eint__mul,type,
    c_2Einteger_2Eint__mul: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__neg,type,
    c_2Einteger_2Eint__neg: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__of__num,type,
    c_2Einteger_2Eint__of__num: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__sub,type,
    c_2Einteger_2Eint__sub: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Ewords_2En2w,type,
    c_2Ewords_2En2w: 
      !>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).

thf(c_2Erealax_2Ereal__add,type,
    c_2Erealax_2Ereal__add: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).

thf(c_2Ereal_2Ereal__ge,type,
    c_2Ereal_2Ereal__ge: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).

thf(c_2Ereal_2Ereal__gt,type,
    c_2Ereal_2Ereal__gt: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).

thf(c_2Erealax_2Ereal__lt,type,
    c_2Erealax_2Ereal__lt: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).

thf(c_2Ereal_2Ereal__lte,type,
    c_2Ereal_2Ereal__lte: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).

thf(c_2Erealax_2Ereal__mul,type,
    c_2Erealax_2Ereal__mul: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).

thf(c_2Erealax_2Ereal__neg,type,
    c_2Erealax_2Ereal__neg: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).

thf(c_2Ereal_2Ereal__of__num,type,
    c_2Ereal_2Ereal__of__num: tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).

thf(c_2Ereal_2Ereal__sub,type,
    c_2Ereal_2Ereal__sub: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).

thf(c_2Ewords_2Esw2sw,type,
    c_2Ewords_2Esw2sw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).

thf(c_2Ebool_2Ethe__value,type,
    c_2Ebool_2Ethe__value: 
      !>[A_27a: $tType] : ( tyop_2Ebool_2Eitself @ A_27a ) ).

thf(c_2Ewords_2Ew2w,type,
    c_2Ewords_2Ew2w: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).

thf(c_2Ewords_2Eword__1comp,type,
    c_2Ewords_2Eword__1comp: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).

thf(c_2Ewords_2Eword__add,type,
    c_2Ewords_2Eword__add: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).

thf(c_2Ewords_2Eword__and,type,
    c_2Ewords_2Eword__and: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).

thf(c_2Ewords_2Eword__concat,type,
    c_2Ewords_2Eword__concat: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) > ( tyop_2Efcp_2Ecart @ $o @ A_27c ) ) ).

thf(c_2Ewords_2Eword__extract,type,
    c_2Ewords_2Eword__extract: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).

thf(c_2Ewords_2Eword__lo,type,
    c_2Ewords_2Eword__lo: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).

thf(c_2Ewords_2Eword__ls,type,
    c_2Ewords_2Eword__ls: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).

thf(c_2Ewords_2Eword__mul,type,
    c_2Ewords_2Eword__mul: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).

thf(c_2Ewords_2Eword__or,type,
    c_2Ewords_2Eword__or: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).

thf(c_2EHolSmt_2Exor,type,
    c_2EHolSmt_2Exor: $o > $o > $o ).

thf(c_2Ebool_2E_7E,type,
    c_2Ebool_2E_7E: $o > $o ).

thf(logicdef_2E_2F_5C,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
    <=> ( V0
        & V1 ) ) ).

thf(logicdef_2E_5C_2F,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
    <=> ( V0
        | V1 ) ) ).

thf(logicdef_2E_7E,axiom,
    ! [V0: $o] :
      ( ( c_2Ebool_2E_7E @ V0 )
    <=> ( (~) @ V0 ) ) ).

thf(logicdef_2E_3D_3D_3E,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
    <=> ( V0
       => V1 ) ) ).

thf(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
      ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
    <=> ( V0 = V1 ) ) ).

thf(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f: A_27a > $o] :
      ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
    <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).

thf(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f: A_27a > $o] :
      ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
    <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).

thf(thm_2EHolSmt_2Exor__def,axiom,
    ! [V0x: $o,V1y: $o] :
      ( ( c_2EHolSmt_2Exor @ V0x @ V1y )
    <=> ( (~) @ ( V0x = V1y ) ) ) ).

thf(thm_2EHolSmt_2Earray__ext__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0A: A_27a > A_27b,V1B: A_27a > A_27b] :
      ( ( c_2EHolSmt_2Earray__ext @ A_27a @ A_27b @ V0A @ V1B )
      = ( c_2Emin_2E_40 @ A_27a
        @ ^ [V2i: A_27a] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ A_27b @ ( V0A @ V2i ) @ ( V1B @ V2i ) ) ) ) ) ).

thf(thm_2EHolSmt_2EALL__DISTINCT__NIL,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2ENIL @ A_27a ) )
      = c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2EALL__DISTINCT__CONS,axiom,
    ! [A_27a: $tType,V0h: A_27a,V1t: tyop_2Elist_2Elist @ A_27a] :
      ( ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V0h @ V1t ) )
    <=> ( ( (~) @ ( c_2Ebool_2EIN @ A_27a @ V0h @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1t ) ) )
        & ( c_2Elist_2EALL__DISTINCT @ A_27a @ V1t ) ) ) ).

thf(thm_2EHolSmt_2ENOT__MEM__NIL,axiom,
    ! [A_27a: $tType,V0x: A_27a] :
      ( ( (~) @ ( c_2Ebool_2EIN @ A_27a @ V0x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
    <=> c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2ENOT__MEM__CONS,axiom,
    ! [A_27a: $tType,V0x: A_27a,V1h: A_27a,V2t: tyop_2Elist_2Elist @ A_27a] :
      ( ( (~) @ ( c_2Ebool_2EIN @ A_27a @ V0x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V1h @ V2t ) ) ) )
    <=> ( ( (~) @ ( V0x = V1h ) )
        & ( (~) @ ( c_2Ebool_2EIN @ A_27a @ V0x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V2t ) ) ) ) ) ).

thf(thm_2EHolSmt_2EAND__T,axiom,
    ! [V0p: $o] :
      ( ( V0p
        & c_2Ebool_2ET )
    <=> V0p ) ).

thf(thm_2EHolSmt_2ET__AND,axiom,
    ! [V0p: $o,V1q: $o] :
      ( ( ( c_2Ebool_2ET
          & V0p )
      <=> ( c_2Ebool_2ET
          & V1q ) )
     => ( V0p = V1q ) ) ).

thf(thm_2EHolSmt_2EF__OR,axiom,
    ! [V0p: $o,V1q: $o] :
      ( ( ( c_2Ebool_2EF
          | V0p )
      <=> ( c_2Ebool_2EF
          | V1q ) )
     => ( V0p = V1q ) ) ).

thf(thm_2EHolSmt_2ECONJ__CONG,axiom,
    ! [V0p: $o,V1q: $o,V2r: $o,V3s: $o] :
      ( ( V0p = V1q )
     => ( ( V2r = V3s )
       => ( ( V0p
            & V2r )
        <=> ( V1q
            & V3s ) ) ) ) ).

thf(thm_2EHolSmt_2ENOT__NOT__ELIM,axiom,
    ! [V0p: $o] :
      ( ( (~) @ ( (~) @ V0p ) )
     => V0p ) ).

thf(thm_2EHolSmt_2ENOT__FALSE,axiom,
    ! [V0p: $o] :
      ( V0p
     => ( ( (~) @ V0p )
       => c_2Ebool_2EF ) ) ).

thf(thm_2EHolSmt_2ENNF__CONJ,axiom,
    ! [V0p: $o,V1q: $o,V2r: $o,V3s: $o] :
      ( ( ( (~) @ V0p )
      <=> V2r )
     => ( ( ( (~) @ V1q )
        <=> V3s )
       => ( ( (~)
            @ ( V0p
              & V1q ) )
        <=> ( V2r
            | V3s ) ) ) ) ).

thf(thm_2EHolSmt_2ENNF__DISJ,axiom,
    ! [V0p: $o,V1q: $o,V2r: $o,V3s: $o] :
      ( ( ( (~) @ V0p )
      <=> V2r )
     => ( ( ( (~) @ V1q )
        <=> V3s )
       => ( ( (~)
            @ ( V0p
              | V1q ) )
        <=> ( V2r
            & V3s ) ) ) ) ).

thf(thm_2EHolSmt_2ENNF__NOT__NOT,axiom,
    ! [V0p: $o,V1q: $o] :
      ( ( V0p = V1q )
     => ( ( (~) @ ( (~) @ V0p ) )
      <=> V1q ) ) ).

thf(thm_2EHolSmt_2ENEG__IFF__1__1,axiom,
    ! [V0p: $o,V1q: $o] :
      ( ( V1q = V0p )
     => ( (~)
        @ ( V0p
        <=> ( (~) @ V1q ) ) ) ) ).

thf(thm_2EHolSmt_2ENEG__IFF__1__2,axiom,
    ! [V0p: $o,V1q: $o] :
      ( ( (~)
        @ ( V0p
        <=> ( (~) @ V1q ) ) )
     => ( V1q = V0p ) ) ).

thf(thm_2EHolSmt_2ENEG__IFF__2__1,axiom,
    ! [V0p: $o,V1q: $o] :
      ( ( V0p
      <=> ( (~) @ V1q ) )
     => ( (~) @ ( V0p = V1q ) ) ) ).

thf(thm_2EHolSmt_2ENEG__IFF__2__2,axiom,
    ! [V0p: $o,V1q: $o] :
      ( ( (~) @ ( V0p = V1q ) )
     => ( V0p
      <=> ( (~) @ V1q ) ) ) ).

thf(thm_2EHolSmt_2EDISJ__ELIM__1,axiom,
    ! [V0p: $o,V1q: $o,V2r: $o] :
      ( ( ( V0p
          | V1q )
       => V2r )
     => ( V0p
       => V2r ) ) ).

thf(thm_2EHolSmt_2EDISJ__ELIM__2,axiom,
    ! [V0p: $o,V1q: $o,V2r: $o] :
      ( ( ( V0p
          | V1q )
       => V2r )
     => ( V1q
       => V2r ) ) ).

thf(thm_2EHolSmt_2EIMP__DISJ__1,axiom,
    ! [V0p: $o,V1q: $o] :
      ( ( V0p
       => V1q )
     => ( ( (~) @ V0p )
        | V1q ) ) ).

thf(thm_2EHolSmt_2EIMP__DISJ__2,axiom,
    ! [V0p: $o,V1q: $o] :
      ( ( ( (~) @ V0p )
       => V1q )
     => ( V0p
        | V1q ) ) ).

thf(thm_2EHolSmt_2EIMP__FALSE,axiom,
    ! [V0p: $o] :
      ( ( ( (~) @ V0p )
       => c_2Ebool_2EF )
     => V0p ) ).

thf(thm_2EHolSmt_2EAND__IMP__INTRO__SYM,axiom,
    ! [V0p: $o,V1q: $o,V2r: $o] :
      ( ( ( V0p
          & V1q )
       => V2r )
    <=> ( V0p
       => ( V1q
         => V2r ) ) ) ).

thf(thm_2EHolSmt_2EVALID__IFF__TRUE,axiom,
    ! [V0p: $o] :
      ( V0p
     => ( V0p = c_2Ebool_2ET ) ) ).

thf(thm_2EHolSmt_2Ed001,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( (~) @ ( V1p = V0q ) )
      | ( (~) @ V1p )
      | V0q ) ).

thf(thm_2EHolSmt_2Ed002,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( (~) @ ( V1p = V0q ) )
      | V1p
      | ( (~) @ V0q ) ) ).

thf(thm_2EHolSmt_2Ed003,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
      <=> ( (~) @ V0q ) )
      | ( (~) @ V1p )
      | V0q ) ).

thf(thm_2EHolSmt_2Ed004,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( ( (~) @ V1p )
      <=> V0q )
      | V1p
      | ( (~) @ V0q ) ) ).

thf(thm_2EHolSmt_2Ed005,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p = V0q )
      | ( (~) @ V1p )
      | ( (~) @ V0q ) ) ).

thf(thm_2EHolSmt_2Ed006,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p = V0q )
      | V1p
      | V0q ) ).

thf(thm_2EHolSmt_2Ed007,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( (~)
        @ ( ( (~) @ V1p )
        <=> V0q ) )
      | V1p
      | V0q ) ).

thf(thm_2EHolSmt_2Ed008,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( (~)
        @ ( V1p
        <=> ( (~) @ V0q ) ) )
      | V1p
      | V0q ) ).

thf(thm_2EHolSmt_2Ed009,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( (~) @ V1p )
      | V0q
      | ( (~) @ ( V1p = V0q ) ) ) ).

thf(thm_2EHolSmt_2Ed010,axiom,
    ! [V0q: $o,V1p: $o] :
      ( V1p
      | ( (~) @ V0q )
      | ( (~) @ ( V1p = V0q ) ) ) ).

thf(thm_2EHolSmt_2Ed011,axiom,
    ! [V0q: $o,V1p: $o] :
      ( V1p
      | V0q
      | ( (~)
        @ ( ( (~) @ V1p )
        <=> V0q ) ) ) ).

thf(thm_2EHolSmt_2Ed012,axiom,
    ! [V0q: $o,V1p: $o] :
      ( V1p
      | V0q
      | ( (~)
        @ ( V1p
        <=> ( (~) @ V0q ) ) ) ) ).

thf(thm_2EHolSmt_2Ed013,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( ( (~) @ V1p )
        & ( (~) @ V0q ) )
      | V1p
      | V0q ) ).

thf(thm_2EHolSmt_2Ed014,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( ( (~) @ V1p )
        & V0q )
      | V1p
      | ( (~) @ V0q ) ) ).

thf(thm_2EHolSmt_2Ed015,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
        & ( (~) @ V0q ) )
      | ( (~) @ V1p )
      | V0q ) ).

thf(thm_2EHolSmt_2Ed016,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
        & V0q )
      | ( (~) @ V1p )
      | ( (~) @ V0q ) ) ).

thf(thm_2EHolSmt_2Ed017,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2p: $o] :
      ( V2p
      | ( V0y
        = ( c_2Ebool_2ECOND @ A_27a @ V2p @ V1x @ V0y ) ) ) ).

thf(thm_2EHolSmt_2Ed018,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2p: $o] :
      ( ( (~) @ V2p )
      | ( V1x
        = ( c_2Ebool_2ECOND @ A_27a @ V2p @ V1x @ V0y ) ) ) ).

thf(thm_2EHolSmt_2Ed019,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2p: $o] :
      ( V2p
      | ( ( c_2Ebool_2ECOND @ A_27a @ V2p @ V1x @ V0y )
        = V0y ) ) ).

thf(thm_2EHolSmt_2Ed020,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2p: $o] :
      ( ( (~) @ V2p )
      | ( ( c_2Ebool_2ECOND @ A_27a @ V2p @ V1x @ V0y )
        = V1x ) ) ).

thf(thm_2EHolSmt_2Ed021,axiom,
    ! [V0r: $o,V1q: $o,V2p: $o] :
      ( V2p
      | V1q
      | ( (~) @ ( c_2Ebool_2ECOND @ $o @ V2p @ V0r @ V1q ) ) ) ).

thf(thm_2EHolSmt_2Ed022,axiom,
    ! [V0r: $o,V1q: $o,V2p: $o] :
      ( ( (~) @ V2p )
      | V1q
      | ( (~) @ ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ V0r ) ) ) ).

thf(thm_2EHolSmt_2Ed023,axiom,
    ! [V0r: $o,V1q: $o,V2p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ V0r )
      | ( (~) @ V2p )
      | ( (~) @ V1q ) ) ).

thf(thm_2EHolSmt_2Ed024,axiom,
    ! [V0r: $o,V1q: $o,V2p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ V0r )
      | V2p
      | ( (~) @ V0r ) ) ).

thf(thm_2EHolSmt_2Ed025,axiom,
    ! [V0r: $o,V1q: $o,V2p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V2p @ ( c_2Ebool_2E_7E @ V1q ) @ V0r )
      | ( (~) @ V2p )
      | V1q ) ).

thf(thm_2EHolSmt_2Ed026,axiom,
    ! [V0r: $o,V1q: $o,V2p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ ( c_2Ebool_2E_7E @ V0r ) )
      | V2p
      | V0r ) ).

thf(thm_2EHolSmt_2Ed027,axiom,
    ! [V0r: $o,V1q: $o,V2p: $o] :
      ( ( (~) @ ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ V0r ) )
      | ( (~) @ V2p )
      | V1q ) ).

thf(thm_2EHolSmt_2Ed028,axiom,
    ! [V0r: $o,V1q: $o,V2p: $o] :
      ( ( (~) @ ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ V0r ) )
      | V2p
      | V0r ) ).

thf(thm_2EHolSmt_2Er001,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a] :
      ( ( V1x = V0y )
    <=> ( V0y = V1x ) ) ).

thf(thm_2EHolSmt_2Er002,axiom,
    ! [A_27a: $tType,V0x: A_27a] :
      ( ( V0x = V0x )
    <=> c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er003,axiom,
    ! [V0p: $o] :
      ( ( V0p = c_2Ebool_2ET )
    <=> V0p ) ).

thf(thm_2EHolSmt_2Er004,axiom,
    ! [V0p: $o] :
      ( ( c_2Ebool_2ET = V0p )
    <=> V0p ) ).

thf(thm_2EHolSmt_2Er005,axiom,
    ! [V0p: $o] :
      ( ( V0p = c_2Ebool_2EF )
    <=> ( (~) @ V0p ) ) ).

thf(thm_2EHolSmt_2Er006,axiom,
    ! [V0p: $o] :
      ( ( c_2Ebool_2EF = V0p )
    <=> ( (~) @ V0p ) ) ).

thf(thm_2EHolSmt_2Er007,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( ( (~) @ V1p )
      <=> ( (~) @ V0q ) )
    <=> ( V1p = V0q ) ) ).

thf(thm_2EHolSmt_2Er008,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( (~)
        @ ( V1p
        <=> ( (~) @ V0q ) ) )
    <=> ( V1p = V0q ) ) ).

thf(thm_2EHolSmt_2Er009,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( (~)
        @ ( ( (~) @ V1p )
        <=> V0q ) )
    <=> ( V1p = V0q ) ) ).

thf(thm_2EHolSmt_2Er010,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a] :
      ( ( c_2Ebool_2ECOND @ A_27a @ c_2Ebool_2ET @ V1x @ V0y )
      = V1x ) ).

thf(thm_2EHolSmt_2Er011,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a] :
      ( ( c_2Ebool_2ECOND @ A_27a @ c_2Ebool_2EF @ V1x @ V0y )
      = V0y ) ).

thf(thm_2EHolSmt_2Er012,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V1p @ V0q @ c_2Ebool_2ET )
    <=> ( ( (~) @ V1p )
        | V0q ) ) ).

thf(thm_2EHolSmt_2Er013,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V1p @ V0q @ c_2Ebool_2ET )
    <=> ( V0q
        | ( (~) @ V1p ) ) ) ).

thf(thm_2EHolSmt_2Er014,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V1p @ V0q @ ( c_2Ebool_2E_7E @ V0q ) )
    <=> ( V1p = V0q ) ) ).

thf(thm_2EHolSmt_2Er015,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V1p @ V0q @ ( c_2Ebool_2E_7E @ V0q ) )
    <=> ( V0q = V1p ) ) ).

thf(thm_2EHolSmt_2Er016,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V1p @ ( c_2Ebool_2E_7E @ V0q ) @ V0q )
    <=> ( V1p
      <=> ( (~) @ V0q ) ) ) ).

thf(thm_2EHolSmt_2Er017,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V1p @ ( c_2Ebool_2E_7E @ V0q ) @ V0q )
    <=> ( ( (~) @ V0q )
      <=> V1p ) ) ).

thf(thm_2EHolSmt_2Er018,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2p: $o] :
      ( ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_7E @ V2p ) @ V1x @ V0y )
      = ( c_2Ebool_2ECOND @ A_27a @ V2p @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er019,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
      ( ( c_2Ebool_2ECOND @ A_27a @ V3p @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) @ V1x )
      = ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_2F_5C @ V3p @ ( c_2Ebool_2E_7E @ V2q ) ) @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er020,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
      ( ( c_2Ebool_2ECOND @ A_27a @ V3p @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) @ V1x )
      = ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ V2q ) @ V3p ) @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er021,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
      ( ( c_2Ebool_2ECOND @ A_27a @ V3p @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) @ V0y )
      = ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_2F_5C @ V3p @ V2q ) @ V1x @ V0y ) ) ).

thf(thm_2EHolSmt_2Er022,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
      ( ( c_2Ebool_2ECOND @ A_27a @ V3p @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) @ V0y )
      = ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_2F_5C @ V2q @ V3p ) @ V1x @ V0y ) ) ).

thf(thm_2EHolSmt_2Er023,axiom,
    ! [A_27a: $tType,V0z: A_27a,V1y: A_27a,V2x: A_27a,V3p: $o] :
      ( ( c_2Ebool_2ECOND @ A_27a @ V3p @ V2x @ ( c_2Ebool_2ECOND @ A_27a @ V3p @ V1y @ V0z ) )
      = ( c_2Ebool_2ECOND @ A_27a @ V3p @ V2x @ V0z ) ) ).

thf(thm_2EHolSmt_2Er024,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
      ( ( c_2Ebool_2ECOND @ A_27a @ V3p @ V1x @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) )
      = ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_5C_2F @ V3p @ V2q ) @ V1x @ V0y ) ) ).

thf(thm_2EHolSmt_2Er025,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
      ( ( c_2Ebool_2ECOND @ A_27a @ V3p @ V1x @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) )
      = ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_5C_2F @ V2q @ V3p ) @ V1x @ V0y ) ) ).

thf(thm_2EHolSmt_2Er026,axiom,
    ! [A_27a: $tType,V0z: A_27a,V1y: A_27a,V2x: A_27a,V3p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V3p @ ( c_2Emin_2E_3D @ A_27a @ V2x @ V1y ) @ ( c_2Emin_2E_3D @ A_27a @ V2x @ V0z ) )
    <=> ( V2x
        = ( c_2Ebool_2ECOND @ A_27a @ V3p @ V1y @ V0z ) ) ) ).

thf(thm_2EHolSmt_2Er027,axiom,
    ! [A_27a: $tType,V0z: A_27a,V1y: A_27a,V2x: A_27a,V3p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V3p @ ( c_2Emin_2E_3D @ A_27a @ V2x @ V1y ) @ ( c_2Emin_2E_3D @ A_27a @ V1y @ V0z ) )
    <=> ( V1y
        = ( c_2Ebool_2ECOND @ A_27a @ V3p @ V2x @ V0z ) ) ) ).

thf(thm_2EHolSmt_2Er028,axiom,
    ! [A_27a: $tType,V0z: A_27a,V1y: A_27a,V2x: A_27a,V3p: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ V3p @ ( c_2Emin_2E_3D @ A_27a @ V2x @ V1y ) @ ( c_2Emin_2E_3D @ A_27a @ V0z @ V1y ) )
    <=> ( V1y
        = ( c_2Ebool_2ECOND @ A_27a @ V3p @ V2x @ V0z ) ) ) ).

thf(thm_2EHolSmt_2Er029,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( ( (~) @ V1p )
       => V0q )
    <=> ( V1p
        | V0q ) ) ).

thf(thm_2EHolSmt_2Er030,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( ( (~) @ V1p )
       => V0q )
    <=> ( V0q
        | V1p ) ) ).

thf(thm_2EHolSmt_2Er031,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
       => V0q )
    <=> ( ( (~) @ V1p )
        | V0q ) ) ).

thf(thm_2EHolSmt_2Er032,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
       => V0q )
    <=> ( V0q
        | ( (~) @ V1p ) ) ) ).

thf(thm_2EHolSmt_2Er033,axiom,
    ! [V0p: $o] :
      ( ( c_2Ebool_2ET
       => V0p )
    <=> V0p ) ).

thf(thm_2EHolSmt_2Er034,axiom,
    ! [V0p: $o] :
      ( ( V0p
       => c_2Ebool_2ET )
    <=> c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er035,axiom,
    ! [V0p: $o] :
      ( ( c_2Ebool_2EF
       => V0p )
    <=> c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er036,axiom,
    ! [V0p: $o] :
      ( ( V0p
       => V0p )
    <=> c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er037,axiom,
    ! [V0r: $o,V1q: $o,V2p: $o] :
      ( ( ( V2p = V1q )
       => V0r )
    <=> ( V0r
        | ( V1q
        <=> ( (~) @ V2p ) ) ) ) ).

thf(thm_2EHolSmt_2Er038,axiom,
    ( ( (~) @ c_2Ebool_2ET )
  <=> c_2Ebool_2EF ) ).

thf(thm_2EHolSmt_2Er039,axiom,
    ( ( (~) @ c_2Ebool_2EF )
  <=> c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er040,axiom,
    ! [V0p: $o] :
      ( ( (~) @ ( (~) @ V0p ) )
    <=> V0p ) ).

thf(thm_2EHolSmt_2Er041,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
        | V0q )
    <=> ( V0q
        | V1p ) ) ).

thf(thm_2EHolSmt_2Er042,axiom,
    ! [V0p: $o] :
      ( ( V0p
        | c_2Ebool_2ET )
    <=> c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er043,axiom,
    ! [V0p: $o] :
      ( ( V0p
        | ( (~) @ V0p ) )
    <=> c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er044,axiom,
    ! [V0p: $o] :
      ( ( ( (~) @ V0p )
        | V0p )
    <=> c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er045,axiom,
    ! [V0p: $o] :
      ( ( c_2Ebool_2ET
        | V0p )
    <=> c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er046,axiom,
    ! [V0p: $o] :
      ( ( V0p
        | c_2Ebool_2EF )
    <=> V0p ) ).

thf(thm_2EHolSmt_2Er047,axiom,
    ! [V0p: $o] :
      ( ( c_2Ebool_2EF
        | V0p )
    <=> V0p ) ).

thf(thm_2EHolSmt_2Er048,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
        & V0q )
    <=> ( V0q
        & V1p ) ) ).

thf(thm_2EHolSmt_2Er049,axiom,
    ! [V0p: $o] :
      ( ( V0p
        & c_2Ebool_2ET )
    <=> V0p ) ).

thf(thm_2EHolSmt_2Er050,axiom,
    ! [V0p: $o] :
      ( ( c_2Ebool_2ET
        & V0p )
    <=> V0p ) ).

thf(thm_2EHolSmt_2Er051,axiom,
    ! [V0p: $o] :
      ( ( V0p
        & c_2Ebool_2EF )
    <=> c_2Ebool_2EF ) ).

thf(thm_2EHolSmt_2Er052,axiom,
    ! [V0p: $o] :
      ( ( c_2Ebool_2EF
        & V0p )
    <=> c_2Ebool_2EF ) ).

thf(thm_2EHolSmt_2Er053,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
        & V0q )
    <=> ( (~)
        @ ( ( (~) @ V1p )
          | ( (~) @ V0q ) ) ) ) ).

thf(thm_2EHolSmt_2Er054,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( ( (~) @ V1p )
        & V0q )
    <=> ( (~)
        @ ( V1p
          | ( (~) @ V0q ) ) ) ) ).

thf(thm_2EHolSmt_2Er055,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
        & ( (~) @ V0q ) )
    <=> ( (~)
        @ ( ( (~) @ V1p )
          | V0q ) ) ) ).

thf(thm_2EHolSmt_2Er056,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( ( (~) @ V1p )
        & ( (~) @ V0q ) )
    <=> ( (~)
        @ ( V1p
          | V0q ) ) ) ).

thf(thm_2EHolSmt_2Er057,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
        & V0q )
    <=> ( (~)
        @ ( ( (~) @ V0q )
          | ( (~) @ V1p ) ) ) ) ).

thf(thm_2EHolSmt_2Er058,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( ( (~) @ V1p )
        & V0q )
    <=> ( (~)
        @ ( ( (~) @ V0q )
          | V1p ) ) ) ).

thf(thm_2EHolSmt_2Er059,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( V1p
        & ( (~) @ V0q ) )
    <=> ( (~)
        @ ( V0q
          | ( (~) @ V1p ) ) ) ) ).

thf(thm_2EHolSmt_2Er060,axiom,
    ! [V0q: $o,V1p: $o] :
      ( ( ( (~) @ V1p )
        & ( (~) @ V0q ) )
    <=> ( (~)
        @ ( V0q
          | V1p ) ) ) ).

thf(thm_2EHolSmt_2Er061,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x: A_27a,V1f: A_27a > A_27b] :
      ( ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b @ V0x @ ( V1f @ V0x ) @ V1f )
      = V1f ) ).

thf(thm_2EHolSmt_2Er062,axiom,
    ! [A_27a: $tType,V0x: A_27a] :
      ( ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V0x @ ( c_2Elist_2ECONS @ A_27a @ V0x @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
      = c_2Ebool_2EF ) ).

thf(thm_2EHolSmt_2Er063,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a] :
      ( ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V1x @ ( c_2Elist_2ECONS @ A_27a @ V0y @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
    <=> ( (~) @ ( V1x = V0y ) ) ) ).

thf(thm_2EHolSmt_2Er064,axiom,
    ! [A_27a: $tType,V0y: A_27a,V1x: A_27a] :
      ( ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V1x @ ( c_2Elist_2ECONS @ A_27a @ V0y @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
    <=> ( (~) @ ( V0y = V1x ) ) ) ).

thf(thm_2EHolSmt_2Er065,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( V1x = V0y )
    <=> ( ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er066,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( V2x
        = ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
    <=> ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) )
        = V1y ) ) ).

thf(thm_2EHolSmt_2Er067,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( V2x
        = ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) )
    <=> ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ V0z ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er068,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( V2x
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ V0z ) )
    <=> ( ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) @ V2x ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er069,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( V2x
        = ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
    <=> ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er070,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( V2x
        = ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
    <=> ( ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er071,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( V2x
        = ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
    <=> ( ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ V0z ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er072,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( V2x
        = ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
    <=> ( ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) )
        = ( c_2Einteger_2Eint__neg @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er073,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( V2x
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1y ) @ V0z ) )
    <=> ( ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) )
        = V1y ) ) ).

thf(thm_2EHolSmt_2Er074,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x )
        = ( c_2Einteger_2Eint__neg @ V0y ) )
    <=> ( V1x = V0y ) ) ).

thf(thm_2EHolSmt_2Er075,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ V1y )
        = V0z )
    <=> ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) )
        = ( c_2Einteger_2Eint__neg @ V0z ) ) ) ).

thf(thm_2EHolSmt_2Er076,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ V1x @ V0y )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    <=> ( V0y
        = ( c_2Einteger_2Eint__neg @ V1x ) ) ) ).

thf(thm_2EHolSmt_2Er077,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ V2x @ V1y )
        = V0z )
    <=> ( ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) )
        = ( c_2Einteger_2Eint__neg @ V2x ) ) ) ).

thf(thm_2EHolSmt_2Er078,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint,V3w: tyop_2Einteger_2Eint,V4v: tyop_2Einteger_2Eint,V5a: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ V5a @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ V4v @ V1y ) @ ( c_2Einteger_2Eint__mul @ V3w @ V0z ) ) ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    <=> ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ V4v ) @ V1y ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ V3w ) @ V0z ) ) )
        = V5a ) ) ).

thf(thm_2EHolSmt_2Er079,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V0x )
      = V0x ) ).

thf(thm_2EHolSmt_2Er080,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = V0x ) ).

thf(thm_2EHolSmt_2Er081,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ V1x @ V0y )
      = ( c_2Einteger_2Eint__add @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er082,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ V0x @ V0x )
      = ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V0x ) ) ).

thf(thm_2EHolSmt_2Er083,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z )
      = ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) ) ) ).

thf(thm_2EHolSmt_2Er084,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z )
      = ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V0z @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er085,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
      = ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V0z @ V2x ) ) ) ).

thf(thm_2EHolSmt_2Er086,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
      = ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V2x @ V0z ) ) ) ).

thf(thm_2EHolSmt_2Er087,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint,V3u: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V0z @ V3u ) ) )
      = ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__add @ V3u @ V2x ) ) ) ) ).

thf(thm_2EHolSmt_2Er088,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__ge @ V0x @ V0x )
      = c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er089,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__ge @ V1x @ V0y )
      = ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er090,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__ge @ V1x @ V0y )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er091,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__ge @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er092,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0x ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er093,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) @ ( c_2Einteger_2Eint__neg @ V0y ) )
      = ( c_2Einteger_2Eint__le @ V1x @ V0y ) ) ).

thf(thm_2EHolSmt_2Er094,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) @ V0y ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er095,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__le @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er096,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__gt @ V1x @ V0y )
    <=> ( (~) @ ( c_2Einteger_2Eint__ge @ V0y @ V1x ) ) ) ).

thf(thm_2EHolSmt_2Er097,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__gt @ V1x @ V0y )
    <=> ( (~) @ ( c_2Einteger_2Eint__le @ V1x @ V0y ) ) ) ).

thf(thm_2EHolSmt_2Er098,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__gt @ V1x @ V0y )
    <=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er099,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__gt @ V1x @ V0y )
    <=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V0y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er100,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__gt @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
    <=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) @ ( c_2Einteger_2Eint__neg @ V1y ) ) ) ) ).

thf(thm_2EHolSmt_2Er101,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ V0x @ V0x )
      = c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er102,axiom,
    ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
    = c_2Ebool_2ET ) ).

thf(thm_2EHolSmt_2Er103,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ V1x @ V0y )
      = ( c_2Einteger_2Eint__ge @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er104,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1x ) @ V0y ) )
      = ( c_2Einteger_2Eint__ge @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er105,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0x ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__ge @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er106,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ V1x @ V0y )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er107,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ V1x @ V0y )
      = ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V0y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er108,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) @ V0y ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er109,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ V1y ) @ ( c_2Einteger_2Eint__neg @ V0z ) )
      = ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) ) @ V0z ) ) ).

thf(thm_2EHolSmt_2Er110,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V2x ) @ V1y ) @ V0z )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) @ V2x ) ) ).

thf(thm_2EHolSmt_2Er111,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) ) @ V0z )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er112,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) @ V1y ) ) ).

thf(thm_2EHolSmt_2Er113,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
      = ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) @ ( c_2Einteger_2Eint__neg @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er114,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er115,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ V1x @ V0y )
    <=> ( (~) @ ( c_2Einteger_2Eint__le @ V0y @ V1x ) ) ) ).

thf(thm_2EHolSmt_2Er116,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ V1x @ V0y )
    <=> ( (~) @ ( c_2Einteger_2Eint__ge @ V1x @ V0y ) ) ) ).

thf(thm_2EHolSmt_2Er117,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ V1x @ V0y )
    <=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er118,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ V1x @ V0y )
    <=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er119,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) )
    <=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) ) @ V0z ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er120,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) )
    <=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ V0z ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er121,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1y ) @ V0z ) )
    <=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er122,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint,V3u: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1y ) @ ( c_2Einteger_2Eint__add @ V0z @ V3u ) ) )
    <=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__add @ V3u @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) ) @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er123,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint,V3v: tyop_2Einteger_2Eint,V4u: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1y ) @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__add @ V4u @ V3v ) ) ) )
    <=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__add @ V4u @ ( c_2Einteger_2Eint__add @ V3v @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) ) ) @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er124,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V2x ) @ V1y ) @ V0z )
    <=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) @ V2x ) ) ) ).

thf(thm_2EHolSmt_2Er125,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z )
    <=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) ) @ V2x ) ) ) ).

thf(thm_2EHolSmt_2Er126,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1x ) @ V0y ) )
    <=> ( (~) @ ( c_2Einteger_2Eint__le @ V0y @ V1x ) ) ) ).

thf(thm_2EHolSmt_2Er127,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = V0x ) ).

thf(thm_2EHolSmt_2Er128,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V0x )
      = ( c_2Einteger_2Eint__neg @ V0x ) ) ).

thf(thm_2EHolSmt_2Er129,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V0x )
      = ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0x ) ) ).

thf(thm_2EHolSmt_2Er130,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ V1x @ V0y )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V0y ) @ V1x ) ) ).

thf(thm_2EHolSmt_2Er131,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ V1x @ V0y )
      = ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) ) ).

thf(thm_2EHolSmt_2Er132,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ V1x @ V0y )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) @ V1x ) ) ).

thf(thm_2EHolSmt_2Er133,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ V0x @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0x ) ) ).

thf(thm_2EHolSmt_2Er134,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z )
      = ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) ) ) ).

thf(thm_2EHolSmt_2Er135,axiom,
    ! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z )
      = ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er136,axiom,
    ! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 )
        = ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) )
    <=> ( ( c_2Erealax_2Ereal__mul @ V1u @ V0x )
        = ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er137,axiom,
    ! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal,V2a: tyop_2Erealax_2Ereal] :
      ( ( V2a
        = ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) )
    <=> ( ( c_2Erealax_2Ereal__mul @ V1u @ V0x )
        = ( c_2Erealax_2Ereal__neg @ V2a ) ) ) ).

thf(thm_2EHolSmt_2Er138,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3a: tyop_2Erealax_2Ereal] :
      ( ( V3a
        = ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V3a ) @ V0z ) ) )
        = ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er139,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3a: tyop_2Erealax_2Ereal] :
      ( ( V3a
        = ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__add @ V0z @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V3a ) ) ) )
        = ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er140,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( V4a
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0z ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1y ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0z ) @ V4a ) )
        = ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er141,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( V4a
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0z ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1y ) @ ( c_2Erealax_2Ereal__add @ V4a @ ( c_2Erealax_2Ereal__mul @ V2v @ V0z ) ) )
        = ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er142,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Erealax_2Ereal__neg @ V4a )
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) )
        = V4a ) ) ).

thf(thm_2EHolSmt_2Er143,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( V6a
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) @ V6a ) ) )
        = ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er144,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( V6a
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
        = ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er145,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( V6a
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
        = ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er146,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( V6a
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
        = ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er147,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( V6a
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
        = ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er148,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Erealax_2Ereal__neg @ V6a )
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
        = V6a ) ) ).

thf(thm_2EHolSmt_2Er149,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Erealax_2Ereal__neg @ V6a )
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
        = V6a ) ) ).

thf(thm_2EHolSmt_2Er150,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Erealax_2Ereal__neg @ V6a )
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
        = V6a ) ) ).

thf(thm_2EHolSmt_2Er151,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Erealax_2Ereal__neg @ V6a )
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
        = V6a ) ) ).

thf(thm_2EHolSmt_2Er152,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4u: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( V5a
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4u @ V2x ) @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
        = ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ).

thf(thm_2EHolSmt_2Er153,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4u: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( V5a
        = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4u @ V2x ) @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
        = ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ).

thf(thm_2EHolSmt_2Er154,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) )
        = ( c_2Erealax_2Ereal__neg @ V4a ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) )
        = V4a ) ) ).

thf(thm_2EHolSmt_2Er155,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
        = ( c_2Erealax_2Ereal__neg @ V5a ) )
    <=> ( ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
        = V5a ) ) ).

thf(thm_2EHolSmt_2Er156,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
        = ( c_2Erealax_2Ereal__neg @ V6a ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
        = V6a ) ) ).

thf(thm_2EHolSmt_2Er157,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
        = ( c_2Erealax_2Ereal__neg @ V6a ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
        = V6a ) ) ).

thf(thm_2EHolSmt_2Er158,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
        = ( c_2Erealax_2Ereal__neg @ V6a ) )
    <=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
        = V6a ) ) ).

thf(thm_2EHolSmt_2Er159,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
      = ( c_2Ereal_2Ereal__lte @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er160,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__ge @ V1x @ V0y )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er161,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__gt @ V1x @ V0y )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er162,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ V1x @ V0y )
      = ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er163,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) )
      = ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) @ V1y ) ) ).

thf(thm_2EHolSmt_2Er164,axiom,
    ! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal,V2a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) @ V2a )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__mul @ V1u @ V0x ) @ ( c_2Erealax_2Ereal__neg @ V2a ) ) ) ).

thf(thm_2EHolSmt_2Er165,axiom,
    ! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal,V2a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) @ ( c_2Erealax_2Ereal__neg @ V2a ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__mul @ V1u @ V0x ) @ V2a ) ) ).

thf(thm_2EHolSmt_2Er166,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er167,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ V4a )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) ) ) ).

thf(thm_2EHolSmt_2Er168,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ V4a ) ) ).

thf(thm_2EHolSmt_2Er169,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ V4a )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) ) ) ).

thf(thm_2EHolSmt_2Er170,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ V4a ) ) ).

thf(thm_2EHolSmt_2Er171,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er172,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er173,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er174,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Er175,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er176,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a ) ) ).

thf(thm_2EHolSmt_2Er177,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er178,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a ) ) ).

thf(thm_2EHolSmt_2Er179,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er180,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a ) ) ).

thf(thm_2EHolSmt_2Er181,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er182,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a ) ) ).

thf(thm_2EHolSmt_2Er183,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
      = ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V5a ) ) ).

thf(thm_2EHolSmt_2Er184,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ V1x @ V0y )
    <=> ( (~) @ ( c_2Ereal_2Ereal__ge @ V1x @ V0y ) ) ) ).

thf(thm_2EHolSmt_2Er185,axiom,
    ! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal,V2a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) @ V2a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__mul @ V1u @ V0x ) @ ( c_2Erealax_2Ereal__neg @ V2a ) ) ) ) ).

thf(thm_2EHolSmt_2Er186,axiom,
    ! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal,V2a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) @ ( c_2Erealax_2Ereal__neg @ V2a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__mul @ V1u @ V0x ) @ V2a ) ) ) ).

thf(thm_2EHolSmt_2Er187,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er188,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er189,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ V4a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) ) ) ) ).

thf(thm_2EHolSmt_2Er190,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ V4a ) ) ) ).

thf(thm_2EHolSmt_2Er191,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ V4a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) ) ) ) ).

thf(thm_2EHolSmt_2Er192,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ V4a ) ) ) ).

thf(thm_2EHolSmt_2Er193,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ) ).

thf(thm_2EHolSmt_2Er194,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er195,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ) ).

thf(thm_2EHolSmt_2Er196,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er197,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ) ).

thf(thm_2EHolSmt_2Er198,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er199,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ) ).

thf(thm_2EHolSmt_2Er200,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a ) ) ) ).

thf(thm_2EHolSmt_2Er201,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er202,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Er203,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V5a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ) ).

thf(thm_2EHolSmt_2Er204,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V5a ) ) ) ).

thf(thm_2EHolSmt_2Er205,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V5a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ) ).

thf(thm_2EHolSmt_2Er206,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V5a ) ) ) ).

thf(thm_2EHolSmt_2Er207,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V5a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ) ).

thf(thm_2EHolSmt_2Er208,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V5a ) ) ) ).

thf(thm_2EHolSmt_2Er209,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V5a )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ) ).

thf(thm_2EHolSmt_2Er210,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V5a ) ) ) ).

thf(thm_2EHolSmt_2Er211,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4u: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4u @ V2x ) @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V5a ) ) ) ).

thf(thm_2EHolSmt_2Er212,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3v: tyop_2Erealax_2Ereal,V4u: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
    <=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3v ) @ V1y ) @ V0z ) ) @ V5a ) ) ) ).

thf(thm_2EHolSmt_2Er213,axiom,
    ! [V0x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) @ V0x )
      = V0x ) ).

thf(thm_2EHolSmt_2Er214,axiom,
    ! [V0x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__add @ V0x @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
      = V0x ) ).

thf(thm_2EHolSmt_2Er215,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__add @ V1x @ V0y )
      = ( c_2Erealax_2Ereal__add @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er216,axiom,
    ! [V0x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__add @ V0x @ V0x )
      = ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V0x ) ) ).

thf(thm_2EHolSmt_2Er217,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ V0z )
      = ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) ) ) ).

thf(thm_2EHolSmt_2Er218,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ V0z )
      = ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V0z @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er219,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) )
      = ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__add @ V0z @ V2x ) ) ) ).

thf(thm_2EHolSmt_2Er220,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) )
      = ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__add @ V2x @ V0z ) ) ) ).

thf(thm_2EHolSmt_2Er221,axiom,
    ! [V0x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) @ V0x )
      = ( c_2Erealax_2Ereal__neg @ V0x ) ) ).

thf(thm_2EHolSmt_2Er222,axiom,
    ! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) @ ( c_2Erealax_2Ereal__mul @ V1u @ V0x ) )
      = ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) ) ).

thf(thm_2EHolSmt_2Er223,axiom,
    ! [V0x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ V0x @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
      = V0x ) ).

thf(thm_2EHolSmt_2Er224,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ V1x @ V0y )
      = ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) ) ).

thf(thm_2EHolSmt_2Er225,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ V1x @ V0y )
      = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) @ V1x ) ) ).

thf(thm_2EHolSmt_2Er226,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ V1x @ ( c_2Erealax_2Ereal__mul @ V2u @ V0y ) )
      = ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2u ) @ V0y ) ) ) ).

thf(thm_2EHolSmt_2Er227,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ V1x @ ( c_2Erealax_2Ereal__mul @ V2u @ V0y ) )
      = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2u ) @ V0y ) @ V1x ) ) ).

thf(thm_2EHolSmt_2Er228,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ V0z )
      = ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) ) ) ).

thf(thm_2EHolSmt_2Er229,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ V0z )
      = ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er230,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3u @ V0z ) )
      = ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V0z ) @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er231,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3u @ V0z ) )
      = ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V0z ) @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Er232,axiom,
    ! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
      ( ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3u @ V0z ) )
      = ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V0z ) ) ) ) ).

thf(thm_2EHolSmt_2Er233,axiom,
    ! [V0x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) @ V0x )
      = ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ).

thf(thm_2EHolSmt_2Er234,axiom,
    ! [V0x: tyop_2Erealax_2Ereal] :
      ( ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0x )
      = V0x ) ).

thf(thm_2EHolSmt_2Er235,axiom,
    ! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0x )
      = V0x ) ).

thf(thm_2EHolSmt_2Er236,axiom,
    ! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Ewords_2Eword__add @ A_27a @ V1x @ V0y )
      = ( c_2Ewords_2Eword__add @ A_27a @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er237,axiom,
    ! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0x ) )
      = ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V0x ) ) ).

thf(thm_2EHolSmt_2Er238,axiom,
    ! [A_27a: $tType,V0z: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( ( c_2Ewords_2Eword__add @ A_27a @ V2x @ V0z )
        = ( c_2Ewords_2Eword__add @ A_27a @ V1y @ V2x ) )
    <=> ( V1y = V0z ) ) ).

thf(thm_2EHolSmt_2Er239,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0x @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
     => ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
       => ( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2En2w @ A_27b @ V0x ) )
          = ( c_2Ewords_2En2w @ A_27c @ V0x ) ) ) ) ).

thf(thm_2EHolSmt_2Er240,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0x @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
     => ( ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2En2w @ A_27a @ V0x ) )
        = ( c_2Ewords_2En2w @ A_27b @ V0x ) ) ) ).

thf(thm_2EHolSmt_2Er241,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y: tyop_2Enum_2Enum,V1x: tyop_2Efcp_2Ecart @ $o @ A_27b] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
     => ( ( c_2Eprim__rec_2E_3C @ V0y @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
       => ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
         => ( ( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1x )
              = ( c_2Ewords_2En2w @ A_27c @ V0y ) )
          <=> ( V1x
              = ( c_2Ewords_2En2w @ A_27b @ V0y ) ) ) ) ) ) ).

thf(thm_2EHolSmt_2Er242,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y: tyop_2Enum_2Enum,V1x: tyop_2Efcp_2Ecart @ $o @ A_27b] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
     => ( ( c_2Eprim__rec_2E_3C @ V0y @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
       => ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
         => ( ( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1x )
              = ( c_2Ewords_2En2w @ A_27c @ V0y ) )
          <=> ( ( c_2Ewords_2En2w @ A_27b @ V0y )
              = V1x ) ) ) ) ) ).

thf(thm_2EHolSmt_2Er243,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y: tyop_2Enum_2Enum,V1x: tyop_2Efcp_2Ecart @ $o @ A_27b] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
     => ( ( c_2Eprim__rec_2E_3C @ V0y @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
       => ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
         => ( ( ( c_2Ewords_2En2w @ A_27c @ V0y )
              = ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1x ) )
          <=> ( V1x
              = ( c_2Ewords_2En2w @ A_27b @ V0y ) ) ) ) ) ) ).

thf(thm_2EHolSmt_2Er244,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y: tyop_2Enum_2Enum,V1x: tyop_2Efcp_2Ecart @ $o @ A_27b] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
     => ( ( c_2Eprim__rec_2E_3C @ V0y @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
       => ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
         => ( ( ( c_2Ewords_2En2w @ A_27c @ V0y )
              = ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1x ) )
          <=> ( ( c_2Ewords_2En2w @ A_27b @ V0y )
              = V1x ) ) ) ) ) ).

thf(thm_2EHolSmt_2Er245,axiom,
    ! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Ewords_2Eword__and @ A_27a @ V1x @ V0y )
      = ( c_2Ewords_2Eword__and @ A_27a @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er246,axiom,
    ! [A_27a: $tType,V0z: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Ewords_2Eword__and @ A_27a @ V2x @ ( c_2Ewords_2Eword__and @ A_27a @ V1y @ V0z ) )
      = ( c_2Ewords_2Eword__and @ A_27a @ V1y @ ( c_2Ewords_2Eword__and @ A_27a @ V2x @ V0z ) ) ) ).

thf(thm_2EHolSmt_2Er247,axiom,
    ! [A_27a: $tType,V0z: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Ewords_2Eword__and @ A_27a @ V2x @ ( c_2Ewords_2Eword__and @ A_27a @ V1y @ V0z ) )
      = ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V2x @ V1y ) @ V0z ) ) ).

thf(thm_2EHolSmt_2Er248,axiom,
    ! [V0y: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Ewords_2Eword__and @ tyop_2Eone_2Eone @ V1x @ V0y ) )
    <=> ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
          = V1x )
        & ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
          = V0y ) ) ) ).

thf(thm_2EHolSmt_2Er249,axiom,
    ! [V0y: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Ewords_2Eword__and @ tyop_2Eone_2Eone @ V1x @ V0y ) )
    <=> ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
          = V0y )
        & ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
          = V1x ) ) ) ).

thf(thm_2EHolSmt_2Er250,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )] :
      ( ( c_2Ewords_2Eword__extract @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2Enum_2E0 @ V0x )
      = V0x ) ).

thf(thm_2EHolSmt_2Er251,axiom,
    ! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Ewords_2Eword__lo @ A_27a @ V1x @ V0y )
    <=> ( (~) @ ( c_2Ewords_2Eword__ls @ A_27a @ V0y @ V1x ) ) ) ).

thf(thm_2EHolSmt_2Er252,axiom,
    ! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Ewords_2Eword__mul @ A_27a @ V1x @ V0y )
      = ( c_2Ewords_2Eword__mul @ A_27a @ V0y @ V1x ) ) ).

thf(thm_2EHolSmt_2Er253,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( c_2Ewords_2Eword__extract @ tyop_2Eone_2Eone @ tyop_2Eone_2Eone @ c_2Enum_2E0 @ c_2Enum_2E0 @ V0x )
      = V0x ) ).

thf(thm_2EHolSmt_2Er254,axiom,
    ! [A_27a: $tType,V0z: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V2x @ V1y ) @ V0z )
      = ( c_2Ewords_2Eword__and @ A_27a @ V2x @ ( c_2Ewords_2Eword__and @ A_27a @ V1y @ V0z ) ) ) ).

thf(thm_2EHolSmt_2Er255,axiom,
    ! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0x )
      = V0x ) ).

thf(thm_2EHolSmt_2Et001,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0z: A_27b,V1y: A_27a,V2x: A_27a,V3f: A_27a > A_27b] :
      ( ( V2x = V1y )
      | ( ( V3f @ V2x )
        = ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b @ V1y @ V0z @ V3f @ V2x ) ) ) ).

thf(thm_2EHolSmt_2Et002,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0z: A_27b,V1y: A_27a,V2x: A_27a,V3f: A_27a > A_27b] :
      ( ( V2x = V1y )
      | ( ( V3f @ V1y )
        = ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b @ V2x @ V0z @ V3f @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Et003,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0z: A_27b,V1y: A_27a,V2x: A_27a,V3f: A_27a > A_27b] :
      ( ( V2x = V1y )
      | ( ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b @ V1y @ V0z @ V3f @ V2x )
        = ( V3f @ V2x ) ) ) ).

thf(thm_2EHolSmt_2Et004,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0z: A_27b,V1y: A_27a,V2x: A_27a,V3f: A_27a > A_27b] :
      ( ( V2x = V1y )
      | ( ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b @ V2x @ V0z @ V3f @ V1y )
        = ( V3f @ V1y ) ) ) ).

thf(thm_2EHolSmt_2Et005,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0g: A_27a > A_27b,V1f: A_27a > A_27b] :
      ( ( V1f = V0g )
      | ( (~)
        @ ( ( V1f @ ( c_2EHolSmt_2Earray__ext @ A_27a @ A_27b @ V1f @ V0g ) )
          = ( V0g @ ( c_2EHolSmt_2Earray__ext @ A_27a @ A_27b @ V1f @ V0g ) ) ) ) ) ).

thf(thm_2EHolSmt_2Et006,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( (~) @ ( V1x = V0y ) )
      | ( c_2Einteger_2Eint__le @ V1x @ V0y ) ) ).

thf(thm_2EHolSmt_2Et007,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( (~) @ ( V1x = V0y ) )
      | ( c_2Einteger_2Eint__ge @ V1x @ V0y ) ) ).

thf(thm_2EHolSmt_2Et008,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( (~) @ ( V1x = V0y ) )
      | ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Et009,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( (~) @ ( V1x = V0y ) )
      | ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Et010,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( V1x = V0y )
      | ( (~) @ ( c_2Einteger_2Eint__le @ V1x @ V0y ) )
      | ( (~) @ ( c_2Einteger_2Eint__ge @ V1x @ V0y ) ) ) ).

thf(thm_2EHolSmt_2Et011,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( (~) @ ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
      | ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2EHolSmt_2Et012,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( (~) @ ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
      | ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Et013,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( (~) @ ( c_2Einteger_2Eint__ge @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
      | ( c_2Einteger_2Eint__ge @ V0x @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(thm_2EHolSmt_2Et014,axiom,
    ! [V0x: tyop_2Einteger_2Eint] :
      ( ( (~) @ ( c_2Einteger_2Eint__ge @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
      | ( (~) @ ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(thm_2EHolSmt_2Et015,axiom,
    ! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__ge @ V1x @ V0y )
      | ( c_2Einteger_2Eint__le @ V1x @ V0y ) ) ).

thf(thm_2EHolSmt_2Et016,axiom,
    ! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
      ( ( (~) @ ( V1x = V0y ) )
      | ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Et017,axiom,
    ! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( (~)
      @ ( V0x
        = ( c_2Ewords_2Eword__1comp @ A_27a @ V0x ) ) ) ).

thf(thm_2EHolSmt_2Et018,axiom,
    ! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a,V2i: tyop_2Enum_2Enum] :
      ( ( V1x = V0y )
     => ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1x @ V2i )
       => ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0y @ V2i ) ) ) ).

thf(thm_2EHolSmt_2Et019,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V0x ) )
      | ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 ) ) ).

thf(thm_2EHolSmt_2Et020,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 )
     => ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 )
        = ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V0x ) ) ) ).

thf(thm_2EHolSmt_2Et021,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 )
     => ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = V0x ) ) ).

thf(thm_2EHolSmt_2Et022,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 ) )
     => ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 )
        = V0x ) ) ).

thf(thm_2EHolSmt_2Et023,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 ) )
     => ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V0x ) ) ) ).

thf(thm_2EHolSmt_2Et024,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 )
        = ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V0x ) )
      | ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Et025,axiom,
    ! [V0y: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Ewords_2Eword__or @ tyop_2Eone_2Eone @ ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V1x ) @ ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V0y ) ) )
      | ( (~)
        @ ( ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V1x @ c_2Enum_2E0 ) )
          | ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0y @ c_2Enum_2E0 ) ) ) ) ) ).

thf(thm_2EHolSmt_2Et026,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )] :
      ( ( ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ c_2Enum_2E0 )
        = V0x )
      | ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ c_2Enum_2E0 )
      | ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      | ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      | ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
      | ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
      | ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(thm_2EHolSmt_2Et027,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1p: $o] :
      ( ( ( V0x
          = ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      <=> V1p )
    <=> ( V0x
        = ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1p @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Et028,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1p: $o] :
      ( ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
          = V0x )
      <=> V1p )
    <=> ( V0x
        = ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1p @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Et029,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1p: $o] :
      ( ( V1p
      <=> ( V0x
          = ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
    <=> ( V0x
        = ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1p @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Et030,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1p: $o] :
      ( ( V1p
      <=> ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
          = V0x ) )
    <=> ( V0x
        = ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1p @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Et031,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )] :
      ( ( ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ c_2Enum_2E0 )
        = ( c_2Ewords_2Eword__mul @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ewords_2Esw2sw @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ V0x ) ) )
     => ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EHolSmt_2Et032,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )] :
      ( ( ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ c_2Enum_2E0 )
        = ( c_2Ewords_2Eword__mul @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ewords_2Esw2sw @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ V0x ) ) )
     => ( (~)
        @ ( ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        <=> ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ c_2Enum_2E0 ) ) ) ) ) ).

thf(thm_2EHolSmt_2Et033,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )] :
      ( ( ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ c_2Enum_2E0 )
        = ( c_2Ewords_2Eword__mul @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ewords_2Esw2sw @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ V0x ) ) )
     => ( (~)
        @ ( ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
        <=> ( ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ c_2Enum_2E0 ) )
            & ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(thm_2EHolSmt_2Et034,axiom,
    ! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1x )
        = V0y )
     => ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1x @ c_2Enum_2E0 )
       => ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0y @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EHolSmt_2Et035,axiom,
    ! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
      ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = V0x )
      | ( (~)
        @ ( ( c_2Ewords_2Eword__extract @ tyop_2Eone_2Eone @ tyop_2Eone_2Eone @ c_2Enum_2E0 @ c_2Enum_2E0 @ V0x )
          = ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(thm_2EHolSmt_2Ep001,axiom,
    ! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).

thf(thm_2EHolSmt_2Ep002,axiom,
    ! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).

thf(thm_2EHolSmt_2Ep003,axiom,
    c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).

thf(thm_2EHolSmt_2Ep004,axiom,
    c_2Epred__set_2EFINITE @ tyop_2Eone_2Eone @ ( c_2Epred__set_2EUNIV @ tyop_2Eone_2Eone ) ).

thf(thm_2EHolSmt_2Ep005,axiom,
    c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).

thf(thm_2EHolSmt_2Ep006,axiom,
    c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ).

thf(thm_2EHolSmt_2Ep007,axiom,
    c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ).

thf(thm_2EHolSmt_2Ep008,axiom,
    c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ).

thf(thm_2EHolSmt_2Ep009,axiom,
    c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).

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