ITP001 Axioms: ITP136^7.ax


%------------------------------------------------------------------------------
% File     : ITP136^7 : 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    : ieee.ax [Gau19]
%          : HL4136^7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  291 (  77 unt; 155 typ;   0 def)
%            Number of atoms       :  506 ( 213 equ;  15 cnn)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives : 3306 (  15   ~;  19   |;  82   &;3131   @)
%                                         (  41 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg;3131 nst)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :  272 ( 272   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  151 ( 149 usr;  17 con; 0-6 aty)
%            Number of variables   :  380 (  31   ^ 318   !;  11   ?; 380   :)
%                                         (  20  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Eieee_2Eccode,type,
    tyop_2Eieee_2Eccode: $tType ).

thf(tyop_2Eieee_2Efloat,type,
    tyop_2Eieee_2Efloat: $tType ).

thf(tyop_2Eieee_2Eroundmode,type,
    tyop_2Eieee_2Eroundmode: $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_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: $tType > $tType > $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_2Earithmetic_2E_2A,type,
    c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2E_2B,type,
    c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Epair_2E_2C,type,
    c_2Epair_2E_2C: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).

thf(c_2Earithmetic_2E_2D,type,
    c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Ereal_2E_2F,type,
    c_2Ereal_2E_2F: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).

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_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_2Earithmetic_2E_3E_3D,type,
    c_2Earithmetic_2E_3E_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $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_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_2Ebool_2EDATATYPE,type,
    c_2Ebool_2EDATATYPE: 
      !>[A_27a: $tType] : ( A_27a > $o ) ).

thf(c_2Earithmetic_2EEVEN,type,
    c_2Earithmetic_2EEVEN: tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2EEXP,type,
    c_2Earithmetic_2EEXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Eieee_2EEq,type,
    c_2Eieee_2EEq: tyop_2Eieee_2Eccode ).

thf(c_2Eieee_2EExponent,type,
    c_2Eieee_2EExponent: tyop_2Eieee_2Efloat > tyop_2Enum_2Enum ).

thf(c_2Eieee_2EFinite,type,
    c_2Eieee_2EFinite: tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2EFloat,type,
    c_2Eieee_2EFloat: tyop_2Erealax_2Ereal > tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2EFraction,type,
    c_2Eieee_2EFraction: tyop_2Eieee_2Efloat > tyop_2Enum_2Enum ).

thf(c_2Epred__set_2EGSPEC,type,
    c_2Epred__set_2EGSPEC: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27b > ( tyop_2Epair_2Eprod @ A_27a @ $o ) ) > A_27a > $o ) ).

thf(c_2Eieee_2EGt,type,
    c_2Eieee_2EGt: tyop_2Eieee_2Eccode ).

thf(c_2Ecombin_2EI,type,
    c_2Ecombin_2EI: 
      !>[A_27a: $tType] : ( A_27a > A_27a ) ).

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

thf(c_2Eieee_2EInfinity,type,
    c_2Eieee_2EInfinity: tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2EIsdenormal,type,
    c_2Eieee_2EIsdenormal: tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2EIsintegral,type,
    c_2Eieee_2EIsintegral: tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2EIsnan,type,
    c_2Eieee_2EIsnan: tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2EIsnormal,type,
    c_2Eieee_2EIsnormal: tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2EIszero,type,
    c_2Eieee_2EIszero: tyop_2Eieee_2Efloat > $o ).

thf(c_2Ebool_2ELET,type,
    c_2Ebool_2ELET: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > A_27a > A_27b ) ).

thf(c_2Eieee_2ELt,type,
    c_2Eieee_2ELt: tyop_2Eieee_2Eccode ).

thf(c_2Eieee_2EMinus__infinity,type,
    c_2Eieee_2EMinus__infinity: tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2EMinus__zero,type,
    c_2Eieee_2EMinus__zero: tyop_2Eieee_2Efloat ).

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

thf(c_2Eieee_2EPlus__infinity,type,
    c_2Eieee_2EPlus__infinity: tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2EPlus__zero,type,
    c_2Eieee_2EPlus__zero: tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2EROUNDFLOAT,type,
    c_2Eieee_2EROUNDFLOAT: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).

thf(c_2Enum_2ESUC,type,
    c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Eieee_2ESign,type,
    c_2Eieee_2ESign: tyop_2Eieee_2Efloat > tyop_2Enum_2Enum ).

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

thf(c_2Ebool_2ETYPE__DEFINITION,type,
    c_2Ebool_2ETYPE__DEFINITION: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > A_27a ) > $o ) ).

thf(c_2Eieee_2ETo__nearest,type,
    c_2Eieee_2ETo__nearest: tyop_2Eieee_2Eroundmode ).

thf(c_2Eieee_2ETo__ninfinity,type,
    c_2Eieee_2ETo__ninfinity: tyop_2Eieee_2Eroundmode ).

thf(c_2Eieee_2ETo__pinfinity,type,
    c_2Eieee_2ETo__pinfinity: tyop_2Eieee_2Eroundmode ).

thf(c_2Eieee_2EUlp,type,
    c_2Eieee_2EUlp: tyop_2Eieee_2Efloat > tyop_2Erealax_2Ereal ).

thf(c_2Eieee_2EUn,type,
    c_2Eieee_2EUn: tyop_2Eieee_2Eccode ).

thf(c_2Eieee_2EVal,type,
    c_2Eieee_2EVal: tyop_2Eieee_2Efloat > tyop_2Erealax_2Ereal ).

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_2Ereal_2Eabs,type,
    c_2Ereal_2Eabs: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).

thf(c_2Eieee_2Ebias,type,
    c_2Eieee_2Ebias: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Ebottomfloat,type,
    c_2Eieee_2Ebottomfloat: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Eccode2num,type,
    c_2Eieee_2Eccode2num: tyop_2Eieee_2Eccode > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Eccode__CASE,type,
    c_2Eieee_2Eccode__CASE: 
      !>[A_27a: $tType] : ( tyop_2Eieee_2Eccode > A_27a > A_27a > A_27a > A_27a > A_27a ) ).

thf(c_2Eieee_2Eccode__size,type,
    c_2Eieee_2Eccode__size: tyop_2Eieee_2Eccode > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Eclosest,type,
    c_2Eieee_2Eclosest: 
      !>[A_27a: $tType] : ( ( A_27a > tyop_2Erealax_2Ereal ) > ( A_27a > $o ) > ( A_27a > $o ) > tyop_2Erealax_2Ereal > A_27a ) ).

thf(c_2Eieee_2Edefloat,type,
    c_2Eieee_2Edefloat: tyop_2Eieee_2Efloat > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Eemax,type,
    c_2Eieee_2Eemax: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Eencoding,type,
    c_2Eieee_2Eencoding: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Eexponent,type,
    c_2Eieee_2Eexponent: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Eexpwidth,type,
    c_2Eieee_2Eexpwidth: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Efadd,type,
    c_2Eieee_2Efadd: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Eieee_2Eroundmode > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Efcompare,type,
    c_2Eieee_2Efcompare: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > tyop_2Eieee_2Eccode ).

thf(c_2Eieee_2Efdiv,type,
    c_2Eieee_2Efdiv: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Eieee_2Eroundmode > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Efeq,type,
    c_2Eieee_2Efeq: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Efge,type,
    c_2Eieee_2Efge: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Efgt,type,
    c_2Eieee_2Efgt: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Efintrnd,type,
    c_2Eieee_2Efintrnd: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Eieee_2Eroundmode > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Efle,type,
    c_2Eieee_2Efle: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Efloat,type,
    c_2Eieee_2Efloat: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2Efloat__To__zero,type,
    c_2Eieee_2Efloat__To__zero: tyop_2Eieee_2Eroundmode ).

thf(c_2Eieee_2Efloat__abs,type,
    c_2Eieee_2Efloat__abs: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2Efloat__add,type,
    c_2Eieee_2Efloat__add: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2Efloat__div,type,
    c_2Eieee_2Efloat__div: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2Efloat__eq,type,
    c_2Eieee_2Efloat__eq: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2Efloat__format,type,
    c_2Eieee_2Efloat__format: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ).

thf(c_2Eieee_2Efloat__ge,type,
    c_2Eieee_2Efloat__ge: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2Efloat__gt,type,
    c_2Eieee_2Efloat__gt: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2Efloat__le,type,
    c_2Eieee_2Efloat__le: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2Efloat__lt,type,
    c_2Eieee_2Efloat__lt: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat > $o ).

thf(c_2Eieee_2Efloat__mul,type,
    c_2Eieee_2Efloat__mul: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2Efloat__neg,type,
    c_2Eieee_2Efloat__neg: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2Efloat__rem,type,
    c_2Eieee_2Efloat__rem: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2Efloat__sqrt,type,
    c_2Eieee_2Efloat__sqrt: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2Efloat__sub,type,
    c_2Eieee_2Efloat__sub: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).

thf(c_2Eieee_2Eflt,type,
    c_2Eieee_2Eflt: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Efmul,type,
    c_2Eieee_2Efmul: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Eieee_2Eroundmode > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Efneg,type,
    c_2Eieee_2Efneg: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Eieee_2Eroundmode > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Efraction,type,
    c_2Eieee_2Efraction: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Efracwidth,type,
    c_2Eieee_2Efracwidth: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Efrem,type,
    c_2Eieee_2Efrem: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Eieee_2Eroundmode > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Efsqrt,type,
    c_2Eieee_2Efsqrt: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Eieee_2Eroundmode > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Efsub,type,
    c_2Eieee_2Efsub: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Eieee_2Eroundmode > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Eintround,type,
    c_2Eieee_2Eintround: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Eieee_2Eroundmode > tyop_2Erealax_2Ereal > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Erealax_2Einv,type,
    c_2Erealax_2Einv: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).

thf(c_2Eieee_2Eis__closest,type,
    c_2Eieee_2Eis__closest: 
      !>[A_27a: $tType] : ( ( A_27a > tyop_2Erealax_2Ereal ) > ( A_27a > $o ) > tyop_2Erealax_2Ereal > A_27a > $o ) ).

thf(c_2Eieee_2Eis__denormal,type,
    c_2Eieee_2Eis__denormal: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Eis__double,type,
    c_2Eieee_2Eis__double: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > $o ).

thf(c_2Eieee_2Eis__double__extended,type,
    c_2Eieee_2Eis__double__extended: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > $o ).

thf(c_2Eieee_2Eis__finite,type,
    c_2Eieee_2Eis__finite: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Eis__infinity,type,
    c_2Eieee_2Eis__infinity: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Eis__integral,type,
    c_2Eieee_2Eis__integral: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Eis__nan,type,
    c_2Eieee_2Eis__nan: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Eis__normal,type,
    c_2Eieee_2Eis__normal: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Eis__single,type,
    c_2Eieee_2Eis__single: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > $o ).

thf(c_2Eieee_2Eis__single__extended,type,
    c_2Eieee_2Eis__single__extended: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > $o ).

thf(c_2Eieee_2Eis__valid,type,
    c_2Eieee_2Eis__valid: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Eis__zero,type,
    c_2Eieee_2Eis__zero: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > $o ).

thf(c_2Eieee_2Elargest,type,
    c_2Eieee_2Elargest: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Erealax_2Ereal ).

thf(c_2Eieee_2Eminus,type,
    c_2Eieee_2Eminus: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Eminus__infinity,type,
    c_2Eieee_2Eminus__infinity: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Eminus__zero,type,
    c_2Eieee_2Eminus__zero: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Enum2ccode,type,
    c_2Eieee_2Enum2ccode: tyop_2Enum_2Enum > tyop_2Eieee_2Eccode ).

thf(c_2Eieee_2Enum2roundmode,type,
    c_2Eieee_2Enum2roundmode: tyop_2Enum_2Enum > tyop_2Eieee_2Eroundmode ).

thf(c_2Eieee_2Eplus__infinity,type,
    c_2Eieee_2Eplus__infinity: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Eplus__zero,type,
    c_2Eieee_2Eplus__zero: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Ereal_2Epow,type,
    c_2Ereal_2Epow: tyop_2Erealax_2Ereal > tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).

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_2Eieee_2Erem,type,
    c_2Eieee_2Erem: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).

thf(c_2Eieee_2Eround,type,
    c_2Eieee_2Eround: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Eieee_2Eroundmode > tyop_2Erealax_2Ereal > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Eroundmode2num,type,
    c_2Eieee_2Eroundmode2num: tyop_2Eieee_2Eroundmode > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Eroundmode__CASE,type,
    c_2Eieee_2Eroundmode__CASE: 
      !>[A_27a: $tType] : ( tyop_2Eieee_2Eroundmode > A_27a > A_27a > A_27a > A_27a > A_27a ) ).

thf(c_2Eieee_2Eroundmode__size,type,
    c_2Eieee_2Eroundmode__size: tyop_2Eieee_2Eroundmode > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Esign,type,
    c_2Eieee_2Esign: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Esome__nan,type,
    c_2Eieee_2Esome__nan: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Etransc_2Esqrt,type,
    c_2Etransc_2Esqrt: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).

thf(c_2Eieee_2Ethreshold,type,
    c_2Eieee_2Ethreshold: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Erealax_2Ereal ).

thf(c_2Eieee_2Etopfloat,type,
    c_2Eieee_2Etopfloat: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

thf(c_2Eieee_2Eulp,type,
    c_2Eieee_2Eulp: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > tyop_2Erealax_2Ereal ).

thf(c_2Eieee_2Evalof,type,
    c_2Eieee_2Evalof: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > tyop_2Erealax_2Ereal ).

thf(c_2Eieee_2Ewordlength,type,
    c_2Eieee_2Ewordlength: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

thf(c_2Eieee_2Ezerosign,type,
    c_2Eieee_2Ezerosign: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ).

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_2Eieee_2Eexpwidth,axiom,
    ! [V0ew: tyop_2Enum_2Enum,V1fw: tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eexpwidth @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V0ew @ V1fw ) )
      = V0ew ) ).

thf(thm_2Eieee_2Efracwidth,axiom,
    ! [V0ew: tyop_2Enum_2Enum,V1fw: tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Efracwidth @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V0ew @ V1fw ) )
      = V1fw ) ).

thf(thm_2Eieee_2Ewordlength,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Ewordlength @ V0X )
      = ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2B @ ( c_2Eieee_2Eexpwidth @ V0X ) @ ( c_2Eieee_2Efracwidth @ V0X ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).

thf(thm_2Eieee_2Eemax,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eemax @ V0X )
      = ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Eieee_2Eexpwidth @ V0X ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).

thf(thm_2Eieee_2Ebias,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Ebias @ V0X )
      = ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Eieee_2Eexpwidth @ V0X ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).

thf(thm_2Eieee_2Eis__single,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eis__single @ V0X )
    <=> ( ( ( c_2Eieee_2Eexpwidth @ V0X )
          = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( ( c_2Eieee_2Ewordlength @ V0X )
          = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Eis__double,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eis__double @ V0X )
    <=> ( ( ( c_2Eieee_2Eexpwidth @ V0X )
          = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( ( c_2Eieee_2Ewordlength @ V0X )
          = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Eis__single__extended,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eis__single__extended @ V0X )
    <=> ( ( c_2Earithmetic_2E_3E_3D @ ( c_2Eieee_2Eexpwidth @ V0X ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
        & ( c_2Earithmetic_2E_3E_3D @ ( c_2Eieee_2Ewordlength @ V0X ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Eis__double__extended,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eis__double__extended @ V0X )
    <=> ( ( c_2Earithmetic_2E_3E_3D @ ( c_2Eieee_2Eexpwidth @ V0X ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
        & ( c_2Earithmetic_2E_3E_3D @ ( c_2Eieee_2Ewordlength @ V0X ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Esign,axiom,
    ! [V0s: tyop_2Enum_2Enum,V1e: tyop_2Enum_2Enum,V2f: tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Esign @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1e @ V2f ) ) )
      = V0s ) ).

thf(thm_2Eieee_2Eexponent,axiom,
    ! [V0s: tyop_2Enum_2Enum,V1e: tyop_2Enum_2Enum,V2f: tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eexponent @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1e @ V2f ) ) )
      = V1e ) ).

thf(thm_2Eieee_2Efraction,axiom,
    ! [V0s: tyop_2Enum_2Enum,V1e: tyop_2Enum_2Enum,V2f: tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Efraction @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V1e @ V2f ) ) )
      = V2f ) ).

thf(thm_2Eieee_2Eis__nan,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Eis__nan @ V0X @ V1a )
    <=> ( ( ( c_2Eieee_2Eexponent @ V1a )
          = ( c_2Eieee_2Eemax @ V0X ) )
        & ( (~)
          @ ( ( c_2Eieee_2Efraction @ V1a )
            = c_2Enum_2E0 ) ) ) ) ).

thf(thm_2Eieee_2Eis__infinity,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Eis__infinity @ V0X @ V1a )
    <=> ( ( ( c_2Eieee_2Eexponent @ V1a )
          = ( c_2Eieee_2Eemax @ V0X ) )
        & ( ( c_2Eieee_2Efraction @ V1a )
          = c_2Enum_2E0 ) ) ) ).

thf(thm_2Eieee_2Eis__normal,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Eis__normal @ V0X @ V1a )
    <=> ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Eieee_2Eexponent @ V1a ) )
        & ( c_2Eprim__rec_2E_3C @ ( c_2Eieee_2Eexponent @ V1a ) @ ( c_2Eieee_2Eemax @ V0X ) ) ) ) ).

thf(thm_2Eieee_2Eis__denormal,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Eis__denormal @ V0X @ V1a )
    <=> ( ( ( c_2Eieee_2Eexponent @ V1a )
          = c_2Enum_2E0 )
        & ( (~)
          @ ( ( c_2Eieee_2Efraction @ V1a )
            = c_2Enum_2E0 ) ) ) ) ).

thf(thm_2Eieee_2Eis__zero,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Eis__zero @ V0X @ V1a )
    <=> ( ( ( c_2Eieee_2Eexponent @ V1a )
          = c_2Enum_2E0 )
        & ( ( c_2Eieee_2Efraction @ V1a )
          = c_2Enum_2E0 ) ) ) ).

thf(thm_2Eieee_2Eis__valid,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1s: tyop_2Enum_2Enum,V2e: tyop_2Enum_2Enum,V3f: tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eis__valid @ V0X @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V1s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V2e @ V3f ) ) )
    <=> ( ( c_2Eprim__rec_2E_3C @ V1s @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) )
        & ( c_2Eprim__rec_2E_3C @ V2e @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Eieee_2Eexpwidth @ V0X ) ) )
        & ( c_2Eprim__rec_2E_3C @ V3f @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Eieee_2Efracwidth @ V0X ) ) ) ) ) ).

thf(thm_2Eieee_2Eis__finite,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Eis__finite @ V0X @ V1a )
    <=> ( ( c_2Eieee_2Eis__valid @ V0X @ V1a )
        & ( ( c_2Eieee_2Eis__normal @ V0X @ V1a )
          | ( c_2Eieee_2Eis__denormal @ V0X @ V1a )
          | ( c_2Eieee_2Eis__zero @ V0X @ V1a ) ) ) ) ).

thf(thm_2Eieee_2Eplus__infinity,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eplus__infinity @ V0X )
      = ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ c_2Enum_2E0 @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Eieee_2Eemax @ V0X ) @ c_2Enum_2E0 ) ) ) ).

thf(thm_2Eieee_2Eminus__infinity,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eminus__infinity @ V0X )
      = ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Eieee_2Eemax @ V0X ) @ c_2Enum_2E0 ) ) ) ).

thf(thm_2Eieee_2Eplus__zero,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eplus__zero @ V0X )
      = ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ c_2Enum_2E0 @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Enum_2E0 @ c_2Enum_2E0 ) ) ) ).

thf(thm_2Eieee_2Eminus__zero,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eminus__zero @ V0X )
      = ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Enum_2E0 @ c_2Enum_2E0 ) ) ) ).

thf(thm_2Eieee_2Etopfloat,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Etopfloat @ V0X )
      = ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ c_2Enum_2E0 @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D @ ( c_2Eieee_2Eemax @ V0X ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Eieee_2Efracwidth @ V0X ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(thm_2Eieee_2Ebottomfloat,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Ebottomfloat @ V0X )
      = ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D @ ( c_2Eieee_2Eemax @ V0X ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Eieee_2Efracwidth @ V0X ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(thm_2Eieee_2Eminus,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Eminus @ V0X @ V1a )
      = ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Eieee_2Esign @ V1a ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Eieee_2Eexponent @ V1a ) @ ( c_2Eieee_2Efraction @ V1a ) ) ) ) ).

thf(thm_2Eieee_2Eencoding,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1s: tyop_2Enum_2Enum,V2e: tyop_2Enum_2Enum,V3f: tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Eencoding @ V0X @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V1s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V2e @ V3f ) ) )
      = ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ V1s @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Eieee_2Ewordlength @ V0X ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Earithmetic_2E_2A @ V2e @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Eieee_2Efracwidth @ V0X ) ) ) ) @ V3f ) ) ).

thf(thm_2Eieee_2Evalof,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1s: tyop_2Enum_2Enum,V2e: tyop_2Enum_2Enum,V3f: tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Evalof @ V0X @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V1s @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ V2e @ V3f ) ) )
      = ( c_2Ebool_2ECOND @ tyop_2Erealax_2Ereal @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V2e @ c_2Enum_2E0 ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Epow @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1s ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Eieee_2Ebias @ V0X ) ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ V3f ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Eieee_2Efracwidth @ V0X ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Epow @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1s ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Eieee_2Ebias @ V0X ) ) ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ V3f ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Eieee_2Efracwidth @ V0X ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Elargest,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Elargest @ V0X )
      = ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Eieee_2Eemax @ V0X ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Eieee_2Ebias @ V0X ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Erealax_2Einv @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Eieee_2Efracwidth @ V0X ) ) ) ) ) ) ).

thf(thm_2Eieee_2Ethreshold,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Ethreshold @ V0X )
      = ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Eieee_2Eemax @ V0X ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Eieee_2Ebias @ V0X ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Erealax_2Einv @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Enum_2ESUC @ ( c_2Eieee_2Efracwidth @ V0X ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Eulp,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Eulp @ V0X @ V1a )
      = ( c_2Ereal_2Ereal__sub @ ( c_2Eieee_2Evalof @ V0X @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ c_2Enum_2E0 @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Eieee_2Eexponent @ V1a ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Eieee_2Evalof @ V0X @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ c_2Enum_2E0 @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Eieee_2Eexponent @ V1a ) @ c_2Enum_2E0 ) ) ) ) ) ).

thf(thm_2Eieee_2Eroundmode__TY__DEF,axiom,
    ? [V0rep: tyop_2Eieee_2Eroundmode > tyop_2Enum_2Enum] :
      ( c_2Ebool_2ETYPE__DEFINITION @ tyop_2Enum_2Enum @ tyop_2Eieee_2Eroundmode
      @ ^ [V1n: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      @ V0rep ) ).

thf(thm_2Eieee_2Eroundmode__BIJ,axiom,
    ( ! [V0a: tyop_2Eieee_2Eroundmode] :
        ( ( c_2Eieee_2Enum2roundmode @ ( c_2Eieee_2Eroundmode2num @ V0a ) )
        = V0a )
    & ! [V1r: tyop_2Enum_2Enum] :
        ( ( ^ [V2n: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ V2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
          @ V1r )
      <=> ( ( c_2Eieee_2Eroundmode2num @ ( c_2Eieee_2Enum2roundmode @ V1r ) )
          = V1r ) ) ) ).

thf(thm_2Eieee_2Eroundmode__size__def,axiom,
    ! [V0x: tyop_2Eieee_2Eroundmode] :
      ( ( c_2Eieee_2Eroundmode__size @ V0x )
      = c_2Enum_2E0 ) ).

thf(thm_2Eieee_2Eroundmode__CASE,axiom,
    ! [A_27a: $tType,V0x: tyop_2Eieee_2Eroundmode,V1v0: A_27a,V2v1: A_27a,V3v2: A_27a,V4v3: A_27a] :
      ( ( c_2Eieee_2Eroundmode__CASE @ A_27a @ V0x @ V1v0 @ V2v1 @ V3v2 @ V4v3 )
      = ( ^ [V5m: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ A_27a @ ( c_2Eprim__rec_2E_3C @ V5m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1v0 @ ( c_2Ebool_2ECOND @ A_27a @ ( c_2Eprim__rec_2E_3C @ V5m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V2v1 @ ( c_2Ebool_2ECOND @ A_27a @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V5m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V3v2 @ V4v3 ) ) )
        @ ( c_2Eieee_2Eroundmode2num @ V0x ) ) ) ).

thf(thm_2Eieee_2Eis__closest,axiom,
    ! [A_27a: $tType,V0v: A_27a > tyop_2Erealax_2Ereal,V1s: A_27a > $o,V2x: tyop_2Erealax_2Ereal,V3a: A_27a] :
      ( ( c_2Eieee_2Eis__closest @ A_27a @ V0v @ V1s @ V2x @ V3a )
    <=> ( ( c_2Ebool_2EIN @ A_27a @ V3a @ V1s )
        & ! [V4b: A_27a] :
            ( ( c_2Ebool_2EIN @ A_27a @ V4b @ V1s )
           => ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2Ereal__sub @ ( V0v @ V3a ) @ V2x ) ) @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2Ereal__sub @ ( V0v @ V4b ) @ V2x ) ) ) ) ) ) ).

thf(thm_2Eieee_2Eclosest,axiom,
    ! [A_27a: $tType,V0v: A_27a > tyop_2Erealax_2Ereal,V1p: A_27a > $o,V2s: A_27a > $o,V3x: tyop_2Erealax_2Ereal] :
      ( ( c_2Eieee_2Eclosest @ A_27a @ V0v @ V1p @ V2s @ V3x )
      = ( c_2Emin_2E_40 @ A_27a
        @ ^ [V4a: A_27a] :
            ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__closest @ A_27a @ V0v @ V2s @ V3x @ V4a )
            @ ( c_2Emin_2E_3D_3D_3E
              @ ( c_2Ebool_2E_3F @ A_27a
                @ ^ [V5b: A_27a] : ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__closest @ A_27a @ V0v @ V2s @ V3x @ V5b ) @ ( V1p @ V5b ) ) )
              @ ( V1p @ V4a ) ) ) ) ) ).

thf(thm_2Eieee_2Eround__def,axiom,
    ( ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1x: tyop_2Erealax_2Ereal] :
        ( ( c_2Eieee_2Eround @ V0X @ c_2Eieee_2ETo__nearest @ V1x )
        = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ereal_2Ereal__lte @ V1x @ ( c_2Erealax_2Ereal__neg @ ( c_2Eieee_2Ethreshold @ V0X ) ) ) @ ( c_2Eieee_2Eminus__infinity @ V0X )
          @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ereal_2Ereal__ge @ V1x @ ( c_2Eieee_2Ethreshold @ V0X ) ) @ ( c_2Eieee_2Eplus__infinity @ V0X )
            @ ( c_2Eieee_2Eclosest @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Evalof @ V0X )
              @ ^ [V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Earithmetic_2EEVEN @ ( c_2Eieee_2Efraction @ V2a ) )
              @ ( c_2Epred__set_2EGSPEC @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) )
                @ ^ [V3a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epair_2E_2C @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ $o @ V3a @ ( c_2Eieee_2Eis__finite @ V0X @ V3a ) ) )
              @ V1x ) ) ) )
    & ! [V4X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V5x: tyop_2Erealax_2Ereal] :
        ( ( c_2Eieee_2Eround @ V4X @ c_2Eieee_2Efloat__To__zero @ V5x )
        = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Erealax_2Ereal__lt @ V5x @ ( c_2Erealax_2Ereal__neg @ ( c_2Eieee_2Elargest @ V4X ) ) ) @ ( c_2Eieee_2Ebottomfloat @ V4X )
          @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ereal_2Ereal__gt @ V5x @ ( c_2Eieee_2Elargest @ V4X ) ) @ ( c_2Eieee_2Etopfloat @ V4X )
            @ ( c_2Eieee_2Eclosest @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Evalof @ V4X )
              @ ^ [V6x: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : c_2Ebool_2ET
              @ ( c_2Epred__set_2EGSPEC @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) )
                @ ^ [V7a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epair_2E_2C @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ $o @ V7a @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__finite @ V4X @ V7a ) @ ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ ( c_2Eieee_2Evalof @ V4X @ V7a ) ) @ ( c_2Ereal_2Eabs @ V5x ) ) ) ) )
              @ V5x ) ) ) )
    & ! [V8X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V9x: tyop_2Erealax_2Ereal] :
        ( ( c_2Eieee_2Eround @ V8X @ c_2Eieee_2ETo__pinfinity @ V9x )
        = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Erealax_2Ereal__lt @ V9x @ ( c_2Erealax_2Ereal__neg @ ( c_2Eieee_2Elargest @ V8X ) ) ) @ ( c_2Eieee_2Ebottomfloat @ V8X )
          @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ereal_2Ereal__gt @ V9x @ ( c_2Eieee_2Elargest @ V8X ) ) @ ( c_2Eieee_2Eplus__infinity @ V8X )
            @ ( c_2Eieee_2Eclosest @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Evalof @ V8X )
              @ ^ [V10x: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : c_2Ebool_2ET
              @ ( c_2Epred__set_2EGSPEC @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) )
                @ ^ [V11a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epair_2E_2C @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ $o @ V11a @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__finite @ V8X @ V11a ) @ ( c_2Ereal_2Ereal__ge @ ( c_2Eieee_2Evalof @ V8X @ V11a ) @ V9x ) ) ) )
              @ V9x ) ) ) )
    & ! [V12X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V13x: tyop_2Erealax_2Ereal] :
        ( ( c_2Eieee_2Eround @ V12X @ c_2Eieee_2ETo__ninfinity @ V13x )
        = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Erealax_2Ereal__lt @ V13x @ ( c_2Erealax_2Ereal__neg @ ( c_2Eieee_2Elargest @ V12X ) ) ) @ ( c_2Eieee_2Eminus__infinity @ V12X )
          @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ereal_2Ereal__gt @ V13x @ ( c_2Eieee_2Elargest @ V12X ) ) @ ( c_2Eieee_2Etopfloat @ V12X )
            @ ( c_2Eieee_2Eclosest @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Evalof @ V12X )
              @ ^ [V14x: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : c_2Ebool_2ET
              @ ( c_2Epred__set_2EGSPEC @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) )
                @ ^ [V15a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epair_2E_2C @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ $o @ V15a @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__finite @ V12X @ V15a ) @ ( c_2Ereal_2Ereal__lte @ ( c_2Eieee_2Evalof @ V12X @ V15a ) @ V13x ) ) ) )
              @ V13x ) ) ) ) ) ).

thf(thm_2Eieee_2Eis__integral,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Eis__integral @ V0X @ V1a )
    <=> ( ( c_2Eieee_2Eis__finite @ V0X @ V1a )
        & ? [V2n: tyop_2Enum_2Enum] :
            ( ( c_2Ereal_2Eabs @ ( c_2Eieee_2Evalof @ V0X @ V1a ) )
            = ( c_2Ereal_2Ereal__of__num @ V2n ) ) ) ) ).

thf(thm_2Eieee_2Eintround__def,axiom,
    ( ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1x: tyop_2Erealax_2Ereal] :
        ( ( c_2Eieee_2Eintround @ V0X @ c_2Eieee_2ETo__nearest @ V1x )
        = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ereal_2Ereal__lte @ V1x @ ( c_2Erealax_2Ereal__neg @ ( c_2Eieee_2Ethreshold @ V0X ) ) ) @ ( c_2Eieee_2Eminus__infinity @ V0X )
          @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ereal_2Ereal__ge @ V1x @ ( c_2Eieee_2Ethreshold @ V0X ) ) @ ( c_2Eieee_2Eplus__infinity @ V0X )
            @ ( c_2Eieee_2Eclosest @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Evalof @ V0X )
              @ ^ [V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
                  ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
                  @ ^ [V3n: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Earithmetic_2EEVEN @ V3n ) @ ( c_2Emin_2E_3D @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Eieee_2Evalof @ V0X @ V2a ) ) @ ( c_2Ereal_2Ereal__of__num @ V3n ) ) ) )
              @ ( c_2Epred__set_2EGSPEC @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) )
                @ ^ [V4a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epair_2E_2C @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ $o @ V4a @ ( c_2Eieee_2Eis__integral @ V0X @ V4a ) ) )
              @ V1x ) ) ) )
    & ! [V5X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V6x: tyop_2Erealax_2Ereal] :
        ( ( c_2Eieee_2Eintround @ V5X @ c_2Eieee_2Efloat__To__zero @ V6x )
        = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Erealax_2Ereal__lt @ V6x @ ( c_2Erealax_2Ereal__neg @ ( c_2Eieee_2Elargest @ V5X ) ) ) @ ( c_2Eieee_2Ebottomfloat @ V5X )
          @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ereal_2Ereal__gt @ V6x @ ( c_2Eieee_2Elargest @ V5X ) ) @ ( c_2Eieee_2Etopfloat @ V5X )
            @ ( c_2Eieee_2Eclosest @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Evalof @ V5X )
              @ ^ [V7x: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : c_2Ebool_2ET
              @ ( c_2Epred__set_2EGSPEC @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) )
                @ ^ [V8a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epair_2E_2C @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ $o @ V8a @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__integral @ V5X @ V8a ) @ ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ ( c_2Eieee_2Evalof @ V5X @ V8a ) ) @ ( c_2Ereal_2Eabs @ V6x ) ) ) ) )
              @ V6x ) ) ) )
    & ! [V9X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V10x: tyop_2Erealax_2Ereal] :
        ( ( c_2Eieee_2Eintround @ V9X @ c_2Eieee_2ETo__pinfinity @ V10x )
        = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Erealax_2Ereal__lt @ V10x @ ( c_2Erealax_2Ereal__neg @ ( c_2Eieee_2Elargest @ V9X ) ) ) @ ( c_2Eieee_2Ebottomfloat @ V9X )
          @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ereal_2Ereal__gt @ V10x @ ( c_2Eieee_2Elargest @ V9X ) ) @ ( c_2Eieee_2Eplus__infinity @ V9X )
            @ ( c_2Eieee_2Eclosest @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Evalof @ V9X )
              @ ^ [V11x: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : c_2Ebool_2ET
              @ ( c_2Epred__set_2EGSPEC @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) )
                @ ^ [V12a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epair_2E_2C @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ $o @ V12a @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__integral @ V9X @ V12a ) @ ( c_2Ereal_2Ereal__ge @ ( c_2Eieee_2Evalof @ V9X @ V12a ) @ V10x ) ) ) )
              @ V10x ) ) ) )
    & ! [V13X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V14x: tyop_2Erealax_2Ereal] :
        ( ( c_2Eieee_2Eintround @ V13X @ c_2Eieee_2ETo__ninfinity @ V14x )
        = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Erealax_2Ereal__lt @ V14x @ ( c_2Erealax_2Ereal__neg @ ( c_2Eieee_2Elargest @ V13X ) ) ) @ ( c_2Eieee_2Eminus__infinity @ V13X )
          @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ereal_2Ereal__gt @ V14x @ ( c_2Eieee_2Elargest @ V13X ) ) @ ( c_2Eieee_2Etopfloat @ V13X )
            @ ( c_2Eieee_2Eclosest @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Evalof @ V13X )
              @ ^ [V15x: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : c_2Ebool_2ET
              @ ( c_2Epred__set_2EGSPEC @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) )
                @ ^ [V16a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epair_2E_2C @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ $o @ V16a @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__integral @ V13X @ V16a ) @ ( c_2Ereal_2Ereal__lte @ ( c_2Eieee_2Evalof @ V13X @ V16a ) @ V14x ) ) ) )
              @ V14x ) ) ) ) ) ).

thf(thm_2Eieee_2Esome__nan,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
      ( ( c_2Eieee_2Esome__nan @ V0X )
      = ( c_2Emin_2E_40 @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) )
        @ ^ [V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Eieee_2Eis__nan @ V0X @ V1a ) ) ) ).

thf(thm_2Eieee_2Ezerosign,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1s: tyop_2Enum_2Enum,V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Ezerosign @ V0X @ V1s @ V2a )
      = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Eis__zero @ V0X @ V2a ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V1s @ c_2Enum_2E0 ) @ ( c_2Eieee_2Eplus__zero @ V0X ) @ ( c_2Eieee_2Eminus__zero @ V0X ) ) @ V2a ) ) ).

thf(thm_2Eieee_2Erem,axiom,
    ! [V0x: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal] :
      ( ( c_2Eieee_2Erem @ V0x @ V1y )
      = ( c_2Ebool_2ELET @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal
        @ ^ [V2n: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub @ V0x @ ( c_2Erealax_2Ereal__mul @ V2n @ V1y ) )
        @ ( c_2Eieee_2Eclosest @ tyop_2Erealax_2Ereal @ ( c_2Ecombin_2EI @ tyop_2Erealax_2Ereal )
          @ ^ [V3x: tyop_2Erealax_2Ereal] :
              ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
              @ ^ [V4n: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Earithmetic_2EEVEN @ V4n ) @ ( c_2Emin_2E_3D @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ V3x ) @ ( c_2Ereal_2Ereal__of__num @ V4n ) ) ) )
          @ ( c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal
            @ ^ [V5x: tyop_2Erealax_2Ereal] :
                ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ V5x
                @ ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
                  @ ^ [V6n: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ V5x ) @ ( c_2Ereal_2Ereal__of__num @ V6n ) ) ) ) )
          @ ( c_2Ereal_2E_2F @ V0x @ V1y ) ) ) ) ).

thf(thm_2Eieee_2Efintrnd,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1m: tyop_2Eieee_2Eroundmode,V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efintrnd @ V0X @ V1m @ V2a )
      = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Eis__nan @ V0X @ V2a ) @ ( c_2Eieee_2Esome__nan @ V0X ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ V2a @ ( c_2Eieee_2Ezerosign @ V0X @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Eintround @ V0X @ V1m @ ( c_2Eieee_2Evalof @ V0X @ V2a ) ) ) ) ) ) ).

thf(thm_2Eieee_2Efadd,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1m: tyop_2Eieee_2Eroundmode,V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V3b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efadd @ V0X @ V1m @ V2a @ V3b )
      = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V2a ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V3b ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V3b ) @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Esign @ V3b ) ) ) ) ) ) ) @ ( c_2Eieee_2Esome__nan @ V0X ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ V2a @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Eis__infinity @ V0X @ V3b ) @ V3b @ ( c_2Eieee_2Ezerosign @ V0X @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__zero @ V0X @ V2a ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__zero @ V0X @ V3b ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Esign @ V3b ) ) ) ) @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Eieee_2Eroundmode @ V1m @ c_2Eieee_2ETo__ninfinity ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) ) @ ( c_2Eieee_2Eround @ V0X @ V1m @ ( c_2Erealax_2Ereal__add @ ( c_2Eieee_2Evalof @ V0X @ V2a ) @ ( c_2Eieee_2Evalof @ V0X @ V3b ) ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Efsub,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1m: tyop_2Eieee_2Eroundmode,V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V3b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efsub @ V0X @ V1m @ V2a @ V3b )
      = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V2a ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V3b ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V3b ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Esign @ V3b ) ) ) ) ) ) @ ( c_2Eieee_2Esome__nan @ V0X ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ V2a @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Eis__infinity @ V0X @ V3b ) @ ( c_2Eieee_2Eminus @ V0X @ V3b ) @ ( c_2Eieee_2Ezerosign @ V0X @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__zero @ V0X @ V2a ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__zero @ V0X @ V3b ) @ ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Esign @ V3b ) ) ) ) ) @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Eieee_2Eroundmode @ V1m @ c_2Eieee_2ETo__ninfinity ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) ) @ ( c_2Eieee_2Eround @ V0X @ V1m @ ( c_2Ereal_2Ereal__sub @ ( c_2Eieee_2Evalof @ V0X @ V2a ) @ ( c_2Eieee_2Evalof @ V0X @ V3b ) ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Efmul,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1m: tyop_2Eieee_2Eroundmode,V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V3b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efmul @ V0X @ V1m @ V2a @ V3b )
      = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V2a ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V3b ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__zero @ V0X @ V2a ) @ ( c_2Eieee_2Eis__infinity @ V0X @ V3b ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ ( c_2Eieee_2Eis__zero @ V0X @ V3b ) ) ) ) ) @ ( c_2Eieee_2Esome__nan @ V0X ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ ( c_2Eieee_2Eis__infinity @ V0X @ V3b ) ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Esign @ V3b ) ) @ ( c_2Eieee_2Eplus__infinity @ V0X ) @ ( c_2Eieee_2Eminus__infinity @ V0X ) ) @ ( c_2Eieee_2Ezerosign @ V0X @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Esign @ V3b ) ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Eieee_2Eround @ V0X @ V1m @ ( c_2Erealax_2Ereal__mul @ ( c_2Eieee_2Evalof @ V0X @ V2a ) @ ( c_2Eieee_2Evalof @ V0X @ V3b ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Efdiv,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1m: tyop_2Eieee_2Eroundmode,V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V3b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efdiv @ V0X @ V1m @ V2a @ V3b )
      = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V2a ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V3b ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__zero @ V0X @ V2a ) @ ( c_2Eieee_2Eis__zero @ V0X @ V3b ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ ( c_2Eieee_2Eis__infinity @ V0X @ V3b ) ) ) ) ) @ ( c_2Eieee_2Esome__nan @ V0X ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ ( c_2Eieee_2Eis__zero @ V0X @ V3b ) ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Esign @ V3b ) ) @ ( c_2Eieee_2Eplus__infinity @ V0X ) @ ( c_2Eieee_2Eminus__infinity @ V0X ) ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Eis__infinity @ V0X @ V3b ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Esign @ V3b ) ) @ ( c_2Eieee_2Eplus__zero @ V0X ) @ ( c_2Eieee_2Eminus__zero @ V0X ) ) @ ( c_2Eieee_2Ezerosign @ V0X @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Esign @ V3b ) ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Eieee_2Eround @ V0X @ V1m @ ( c_2Ereal_2E_2F @ ( c_2Eieee_2Evalof @ V0X @ V2a ) @ ( c_2Eieee_2Evalof @ V0X @ V3b ) ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Efsqrt,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1m: tyop_2Eieee_2Eroundmode,V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efsqrt @ V0X @ V1m @ V2a )
      = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Eis__nan @ V0X @ V2a ) @ ( c_2Eieee_2Esome__nan @ V0X ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__zero @ V0X @ V2a ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ c_2Enum_2E0 ) ) ) @ V2a @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Eieee_2Esome__nan @ V0X ) @ ( c_2Eieee_2Ezerosign @ V0X @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Eround @ V0X @ V1m @ ( c_2Etransc_2Esqrt @ ( c_2Eieee_2Evalof @ V0X @ V2a ) ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Efrem,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1m: tyop_2Eieee_2Eroundmode,V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V3b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efrem @ V0X @ V1m @ V2a @ V3b )
      = ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V2a ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V3b ) @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__infinity @ V0X @ V2a ) @ ( c_2Eieee_2Eis__zero @ V0X @ V3b ) ) ) ) @ ( c_2Eieee_2Esome__nan @ V0X ) @ ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( c_2Eieee_2Eis__infinity @ V0X @ V3b ) @ V2a @ ( c_2Eieee_2Ezerosign @ V0X @ ( c_2Eieee_2Esign @ V2a ) @ ( c_2Eieee_2Eround @ V0X @ V1m @ ( c_2Eieee_2Erem @ ( c_2Eieee_2Evalof @ V0X @ V2a ) @ ( c_2Eieee_2Evalof @ V0X @ V3b ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Efneg,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1m: tyop_2Eieee_2Eroundmode,V2a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efneg @ V0X @ V1m @ V2a )
      = ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Eieee_2Esign @ V2a ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Eieee_2Eexponent @ V2a ) @ ( c_2Eieee_2Efraction @ V2a ) ) ) ) ).

thf(thm_2Eieee_2Eccode__TY__DEF,axiom,
    ? [V0rep: tyop_2Eieee_2Eccode > tyop_2Enum_2Enum] :
      ( c_2Ebool_2ETYPE__DEFINITION @ tyop_2Enum_2Enum @ tyop_2Eieee_2Eccode
      @ ^ [V1n: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      @ V0rep ) ).

thf(thm_2Eieee_2Eccode__BIJ,axiom,
    ( ! [V0a: tyop_2Eieee_2Eccode] :
        ( ( c_2Eieee_2Enum2ccode @ ( c_2Eieee_2Eccode2num @ V0a ) )
        = V0a )
    & ! [V1r: tyop_2Enum_2Enum] :
        ( ( ^ [V2n: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ V2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
          @ V1r )
      <=> ( ( c_2Eieee_2Eccode2num @ ( c_2Eieee_2Enum2ccode @ V1r ) )
          = V1r ) ) ) ).

thf(thm_2Eieee_2Eccode__size__def,axiom,
    ! [V0x: tyop_2Eieee_2Eccode] :
      ( ( c_2Eieee_2Eccode__size @ V0x )
      = c_2Enum_2E0 ) ).

thf(thm_2Eieee_2Eccode__CASE,axiom,
    ! [A_27a: $tType,V0x: tyop_2Eieee_2Eccode,V1v0: A_27a,V2v1: A_27a,V3v2: A_27a,V4v3: A_27a] :
      ( ( c_2Eieee_2Eccode__CASE @ A_27a @ V0x @ V1v0 @ V2v1 @ V3v2 @ V4v3 )
      = ( ^ [V5m: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ A_27a @ ( c_2Eprim__rec_2E_3C @ V5m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1v0 @ ( c_2Ebool_2ECOND @ A_27a @ ( c_2Eprim__rec_2E_3C @ V5m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V2v1 @ ( c_2Ebool_2ECOND @ A_27a @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V5m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V3v2 @ V4v3 ) ) )
        @ ( c_2Eieee_2Eccode2num @ V0x ) ) ) ).

thf(thm_2Eieee_2Efcompare,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V2b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efcompare @ V0X @ V1a @ V2b )
      = ( c_2Ebool_2ECOND @ tyop_2Eieee_2Eccode @ ( c_2Ebool_2E_5C_2F @ ( c_2Eieee_2Eis__nan @ V0X @ V1a ) @ ( c_2Eieee_2Eis__nan @ V0X @ V2b ) ) @ c_2Eieee_2EUn @ ( c_2Ebool_2ECOND @ tyop_2Eieee_2Eccode @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V1a ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V1a ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Eieee_2Eccode @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V2b ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2b ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2Eieee_2EEq @ c_2Eieee_2ELt ) @ ( c_2Ebool_2ECOND @ tyop_2Eieee_2Eccode @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V1a ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V1a ) @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2ECOND @ tyop_2Eieee_2Eccode @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V2b ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2b ) @ c_2Enum_2E0 ) ) @ c_2Eieee_2EEq @ c_2Eieee_2EGt ) @ ( c_2Ebool_2ECOND @ tyop_2Eieee_2Eccode @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V2b ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2b ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2Eieee_2EGt @ ( c_2Ebool_2ECOND @ tyop_2Eieee_2Eccode @ ( c_2Ebool_2E_2F_5C @ ( c_2Eieee_2Eis__infinity @ V0X @ V2b ) @ ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ ( c_2Eieee_2Esign @ V2b ) @ c_2Enum_2E0 ) ) @ c_2Eieee_2ELt @ ( c_2Ebool_2ECOND @ tyop_2Eieee_2Eccode @ ( c_2Erealax_2Ereal__lt @ ( c_2Eieee_2Evalof @ V0X @ V1a ) @ ( c_2Eieee_2Evalof @ V0X @ V2b ) ) @ c_2Eieee_2ELt @ ( c_2Ebool_2ECOND @ tyop_2Eieee_2Eccode @ ( c_2Emin_2E_3D @ tyop_2Erealax_2Ereal @ ( c_2Eieee_2Evalof @ V0X @ V1a ) @ ( c_2Eieee_2Evalof @ V0X @ V2b ) ) @ c_2Eieee_2EEq @ c_2Eieee_2EGt ) ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Eflt,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V2b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Eflt @ V0X @ V1a @ V2b )
    <=> ( ( c_2Eieee_2Efcompare @ V0X @ V1a @ V2b )
        = c_2Eieee_2ELt ) ) ).

thf(thm_2Eieee_2Efle,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V2b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efle @ V0X @ V1a @ V2b )
    <=> ( ( ( c_2Eieee_2Efcompare @ V0X @ V1a @ V2b )
          = c_2Eieee_2ELt )
        | ( ( c_2Eieee_2Efcompare @ V0X @ V1a @ V2b )
          = c_2Eieee_2EEq ) ) ) ).

thf(thm_2Eieee_2Efgt,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V2b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efgt @ V0X @ V1a @ V2b )
    <=> ( ( c_2Eieee_2Efcompare @ V0X @ V1a @ V2b )
        = c_2Eieee_2EGt ) ) ).

thf(thm_2Eieee_2Efge,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V2b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efge @ V0X @ V1a @ V2b )
    <=> ( ( ( c_2Eieee_2Efcompare @ V0X @ V1a @ V2b )
          = c_2Eieee_2EGt )
        | ( ( c_2Eieee_2Efcompare @ V0X @ V1a @ V2b )
          = c_2Eieee_2EEq ) ) ) ).

thf(thm_2Eieee_2Efeq,axiom,
    ! [V0X: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,V1a: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),V2b: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
      ( ( c_2Eieee_2Efeq @ V0X @ V1a @ V2b )
    <=> ( ( c_2Eieee_2Efcompare @ V0X @ V1a @ V2b )
        = c_2Eieee_2EEq ) ) ).

thf(thm_2Eieee_2Efloat__format,axiom,
    ( c_2Eieee_2Efloat__format
    = ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(thm_2Eieee_2Efloat__TY__DEF,axiom,
    ? [V0rep: tyop_2Eieee_2Efloat > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) )] : ( c_2Ebool_2ETYPE__DEFINITION @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Eieee_2Efloat @ ( c_2Eieee_2Eis__valid @ c_2Eieee_2Efloat__format ) @ V0rep ) ).

thf(thm_2Eieee_2Efloat__tybij,axiom,
    ( ! [V0a: tyop_2Eieee_2Efloat] :
        ( ( c_2Eieee_2Efloat @ ( c_2Eieee_2Edefloat @ V0a ) )
        = V0a )
    & ! [V1r: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
        ( ( c_2Eieee_2Eis__valid @ c_2Eieee_2Efloat__format @ V1r )
      <=> ( ( c_2Eieee_2Edefloat @ ( c_2Eieee_2Efloat @ V1r ) )
          = V1r ) ) ) ).

thf(thm_2Eieee_2EVal,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EVal @ V0a )
      = ( c_2Eieee_2Evalof @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EFloat,axiom,
    ! [V0x: tyop_2Erealax_2Ereal] :
      ( ( c_2Eieee_2EFloat @ V0x )
      = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Eround @ c_2Eieee_2Efloat__format @ c_2Eieee_2ETo__nearest @ V0x ) ) ) ).

thf(thm_2Eieee_2ESign,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2ESign @ V0a )
      = ( c_2Eieee_2Esign @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EExponent,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EExponent @ V0a )
      = ( c_2Eieee_2Eexponent @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EFraction,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EFraction @ V0a )
      = ( c_2Eieee_2Efraction @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EUlp,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EUlp @ V0a )
      = ( c_2Eieee_2Eulp @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EIsnan,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EIsnan @ V0a )
      = ( c_2Eieee_2Eis__nan @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EInfinity,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EInfinity @ V0a )
      = ( c_2Eieee_2Eis__infinity @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EIsnormal,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EIsnormal @ V0a )
      = ( c_2Eieee_2Eis__normal @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EIsdenormal,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EIsdenormal @ V0a )
      = ( c_2Eieee_2Eis__denormal @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EIszero,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EIszero @ V0a )
      = ( c_2Eieee_2Eis__zero @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EFinite,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EFinite @ V0a )
    <=> ( ( c_2Eieee_2EIsnormal @ V0a )
        | ( c_2Eieee_2EIsdenormal @ V0a )
        | ( c_2Eieee_2EIszero @ V0a ) ) ) ).

thf(thm_2Eieee_2EIsintegral,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EIsintegral @ V0a )
      = ( c_2Eieee_2Eis__integral @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ).

thf(thm_2Eieee_2EPlus__zero,axiom,
    ( c_2Eieee_2EPlus__zero
    = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Eplus__zero @ c_2Eieee_2Efloat__format ) ) ) ).

thf(thm_2Eieee_2EMinus__zero,axiom,
    ( c_2Eieee_2EMinus__zero
    = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Eminus__zero @ c_2Eieee_2Efloat__format ) ) ) ).

thf(thm_2Eieee_2EMinus__infinity,axiom,
    ( c_2Eieee_2EMinus__infinity
    = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Eminus__infinity @ c_2Eieee_2Efloat__format ) ) ) ).

thf(thm_2Eieee_2EPlus__infinity,axiom,
    ( c_2Eieee_2EPlus__infinity
    = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Eplus__infinity @ c_2Eieee_2Efloat__format ) ) ) ).

thf(thm_2Eieee_2Efloat__add,axiom,
    ! [V0a: tyop_2Eieee_2Efloat,V1b: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__add @ V0a @ V1b )
      = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Efadd @ c_2Eieee_2Efloat__format @ c_2Eieee_2ETo__nearest @ ( c_2Eieee_2Edefloat @ V0a ) @ ( c_2Eieee_2Edefloat @ V1b ) ) ) ) ).

thf(thm_2Eieee_2Efloat__sub,axiom,
    ! [V0a: tyop_2Eieee_2Efloat,V1b: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__sub @ V0a @ V1b )
      = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Efsub @ c_2Eieee_2Efloat__format @ c_2Eieee_2ETo__nearest @ ( c_2Eieee_2Edefloat @ V0a ) @ ( c_2Eieee_2Edefloat @ V1b ) ) ) ) ).

thf(thm_2Eieee_2Efloat__mul,axiom,
    ! [V0a: tyop_2Eieee_2Efloat,V1b: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__mul @ V0a @ V1b )
      = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Efmul @ c_2Eieee_2Efloat__format @ c_2Eieee_2ETo__nearest @ ( c_2Eieee_2Edefloat @ V0a ) @ ( c_2Eieee_2Edefloat @ V1b ) ) ) ) ).

thf(thm_2Eieee_2Efloat__div,axiom,
    ! [V0a: tyop_2Eieee_2Efloat,V1b: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__div @ V0a @ V1b )
      = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Efdiv @ c_2Eieee_2Efloat__format @ c_2Eieee_2ETo__nearest @ ( c_2Eieee_2Edefloat @ V0a ) @ ( c_2Eieee_2Edefloat @ V1b ) ) ) ) ).

thf(thm_2Eieee_2Efloat__rem,axiom,
    ! [V0a: tyop_2Eieee_2Efloat,V1b: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__rem @ V0a @ V1b )
      = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Efrem @ c_2Eieee_2Efloat__format @ c_2Eieee_2ETo__nearest @ ( c_2Eieee_2Edefloat @ V0a ) @ ( c_2Eieee_2Edefloat @ V1b ) ) ) ) ).

thf(thm_2Eieee_2Efloat__sqrt,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__sqrt @ V0a )
      = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Efsqrt @ c_2Eieee_2Efloat__format @ c_2Eieee_2ETo__nearest @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ) ).

thf(thm_2Eieee_2EROUNDFLOAT,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2EROUNDFLOAT @ V0a )
      = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Efintrnd @ c_2Eieee_2Efloat__format @ c_2Eieee_2ETo__nearest @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ) ).

thf(thm_2Eieee_2Efloat__lt,axiom,
    ! [V0a: tyop_2Eieee_2Efloat,V1b: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__lt @ V0a @ V1b )
      = ( c_2Eieee_2Eflt @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) @ ( c_2Eieee_2Edefloat @ V1b ) ) ) ).

thf(thm_2Eieee_2Efloat__le,axiom,
    ! [V0a: tyop_2Eieee_2Efloat,V1b: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__le @ V0a @ V1b )
      = ( c_2Eieee_2Efle @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) @ ( c_2Eieee_2Edefloat @ V1b ) ) ) ).

thf(thm_2Eieee_2Efloat__gt,axiom,
    ! [V0a: tyop_2Eieee_2Efloat,V1b: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__gt @ V0a @ V1b )
      = ( c_2Eieee_2Efgt @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) @ ( c_2Eieee_2Edefloat @ V1b ) ) ) ).

thf(thm_2Eieee_2Efloat__ge,axiom,
    ! [V0a: tyop_2Eieee_2Efloat,V1b: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__ge @ V0a @ V1b )
      = ( c_2Eieee_2Efge @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) @ ( c_2Eieee_2Edefloat @ V1b ) ) ) ).

thf(thm_2Eieee_2Efloat__eq,axiom,
    ! [V0a: tyop_2Eieee_2Efloat,V1b: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__eq @ V0a @ V1b )
      = ( c_2Eieee_2Efeq @ c_2Eieee_2Efloat__format @ ( c_2Eieee_2Edefloat @ V0a ) @ ( c_2Eieee_2Edefloat @ V1b ) ) ) ).

thf(thm_2Eieee_2Efloat__neg,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__neg @ V0a )
      = ( c_2Eieee_2Efloat @ ( c_2Eieee_2Efneg @ c_2Eieee_2Efloat__format @ c_2Eieee_2ETo__nearest @ ( c_2Eieee_2Edefloat @ V0a ) ) ) ) ).

thf(thm_2Eieee_2Efloat__abs,axiom,
    ! [V0a: tyop_2Eieee_2Efloat] :
      ( ( c_2Eieee_2Efloat__abs @ V0a )
      = ( c_2Ebool_2ECOND @ tyop_2Eieee_2Efloat @ ( c_2Eieee_2Efloat__ge @ V0a @ c_2Eieee_2EPlus__zero ) @ V0a @ ( c_2Eieee_2Efloat__neg @ V0a ) ) ) ).

thf(thm_2Eieee_2Enum2roundmode__roundmode2num,axiom,
    ! [V0a: tyop_2Eieee_2Eroundmode] :
      ( ( c_2Eieee_2Enum2roundmode @ ( c_2Eieee_2Eroundmode2num @ V0a ) )
      = V0a ) ).

thf(thm_2Eieee_2Eroundmode2num__num2roundmode,axiom,
    ! [V0r: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
    <=> ( ( c_2Eieee_2Eroundmode2num @ ( c_2Eieee_2Enum2roundmode @ V0r ) )
        = V0r ) ) ).

thf(thm_2Eieee_2Enum2roundmode__11,axiom,
    ! [V0r: tyop_2Enum_2Enum,V1r_27: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
     => ( ( c_2Eprim__rec_2E_3C @ V1r_27 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       => ( ( ( c_2Eieee_2Enum2roundmode @ V0r )
            = ( c_2Eieee_2Enum2roundmode @ V1r_27 ) )
        <=> ( V0r = V1r_27 ) ) ) ) ).

thf(thm_2Eieee_2Eroundmode2num__11,axiom,
    ! [V0a: tyop_2Eieee_2Eroundmode,V1a_27: tyop_2Eieee_2Eroundmode] :
      ( ( ( c_2Eieee_2Eroundmode2num @ V0a )
        = ( c_2Eieee_2Eroundmode2num @ V1a_27 ) )
    <=> ( V0a = V1a_27 ) ) ).

thf(thm_2Eieee_2Enum2roundmode__ONTO,axiom,
    ! [V0a: tyop_2Eieee_2Eroundmode] :
    ? [V1r: tyop_2Enum_2Enum] :
      ( ( V0a
        = ( c_2Eieee_2Enum2roundmode @ V1r ) )
      & ( c_2Eprim__rec_2E_3C @ V1r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2Eieee_2Eroundmode2num__ONTO,axiom,
    ! [V0r: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
    <=> ? [V1a: tyop_2Eieee_2Eroundmode] :
          ( V0r
          = ( c_2Eieee_2Eroundmode2num @ V1a ) ) ) ).

thf(thm_2Eieee_2Enum2roundmode__thm,axiom,
    ( ( ( c_2Eieee_2Enum2roundmode @ c_2Enum_2E0 )
      = c_2Eieee_2ETo__nearest )
    & ( ( c_2Eieee_2Enum2roundmode @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Eieee_2Efloat__To__zero )
    & ( ( c_2Eieee_2Enum2roundmode @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Eieee_2ETo__pinfinity )
    & ( ( c_2Eieee_2Enum2roundmode @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = c_2Eieee_2ETo__ninfinity ) ) ).

thf(thm_2Eieee_2Eroundmode2num__thm,axiom,
    ( ( ( c_2Eieee_2Eroundmode2num @ c_2Eieee_2ETo__nearest )
      = c_2Enum_2E0 )
    & ( ( c_2Eieee_2Eroundmode2num @ c_2Eieee_2Efloat__To__zero )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
    & ( ( c_2Eieee_2Eroundmode2num @ c_2Eieee_2ETo__pinfinity )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
    & ( ( c_2Eieee_2Eroundmode2num @ c_2Eieee_2ETo__ninfinity )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2Eieee_2Eroundmode__EQ__roundmode,axiom,
    ! [V0a: tyop_2Eieee_2Eroundmode,V1a_27: tyop_2Eieee_2Eroundmode] :
      ( ( V0a = V1a_27 )
    <=> ( ( c_2Eieee_2Eroundmode2num @ V0a )
        = ( c_2Eieee_2Eroundmode2num @ V1a_27 ) ) ) ).

thf(thm_2Eieee_2Eroundmode__case__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0v0: A_27a,V1v1: A_27a,V2v2: A_27a,V3v3: A_27a] :
          ( ( c_2Eieee_2Eroundmode__CASE @ A_27a @ c_2Eieee_2ETo__nearest @ V0v0 @ V1v1 @ V2v2 @ V3v3 )
          = V0v0 )
      & ! [V4v0: A_27a,V5v1: A_27a,V6v2: A_27a,V7v3: A_27a] :
          ( ( c_2Eieee_2Eroundmode__CASE @ A_27a @ c_2Eieee_2Efloat__To__zero @ V4v0 @ V5v1 @ V6v2 @ V7v3 )
          = V5v1 )
      & ! [V8v0: A_27a,V9v1: A_27a,V10v2: A_27a,V11v3: A_27a] :
          ( ( c_2Eieee_2Eroundmode__CASE @ A_27a @ c_2Eieee_2ETo__pinfinity @ V8v0 @ V9v1 @ V10v2 @ V11v3 )
          = V10v2 )
      & ! [V12v0: A_27a,V13v1: A_27a,V14v2: A_27a,V15v3: A_27a] :
          ( ( c_2Eieee_2Eroundmode__CASE @ A_27a @ c_2Eieee_2ETo__ninfinity @ V12v0 @ V13v1 @ V14v2 @ V15v3 )
          = V15v3 ) ) ).

thf(thm_2Eieee_2Edatatype__roundmode,axiom,
    ! [V0roundmode: tyop_2Eieee_2Eroundmode > tyop_2Eieee_2Eroundmode > tyop_2Eieee_2Eroundmode > tyop_2Eieee_2Eroundmode > $o] : ( c_2Ebool_2EDATATYPE @ $o @ ( V0roundmode @ c_2Eieee_2ETo__nearest @ c_2Eieee_2Efloat__To__zero @ c_2Eieee_2ETo__pinfinity @ c_2Eieee_2ETo__ninfinity ) ) ).

thf(thm_2Eieee_2Eroundmode__distinct,axiom,
    ( ( (~) @ ( c_2Eieee_2ETo__nearest = c_2Eieee_2Efloat__To__zero ) )
    & ( (~) @ ( c_2Eieee_2ETo__nearest = c_2Eieee_2ETo__pinfinity ) )
    & ( (~) @ ( c_2Eieee_2ETo__nearest = c_2Eieee_2ETo__ninfinity ) )
    & ( (~) @ ( c_2Eieee_2Efloat__To__zero = c_2Eieee_2ETo__pinfinity ) )
    & ( (~) @ ( c_2Eieee_2Efloat__To__zero = c_2Eieee_2ETo__ninfinity ) )
    & ( (~) @ ( c_2Eieee_2ETo__pinfinity = c_2Eieee_2ETo__ninfinity ) ) ) ).

thf(thm_2Eieee_2Eroundmode__nchotomy,axiom,
    ! [V0a: tyop_2Eieee_2Eroundmode] :
      ( ( V0a = c_2Eieee_2ETo__nearest )
      | ( V0a = c_2Eieee_2Efloat__To__zero )
      | ( V0a = c_2Eieee_2ETo__pinfinity )
      | ( V0a = c_2Eieee_2ETo__ninfinity ) ) ).

thf(thm_2Eieee_2Eroundmode__Axiom,axiom,
    ! [A_27a: $tType,V0x0: A_27a,V1x1: A_27a,V2x2: A_27a,V3x3: A_27a] :
    ? [V4f: tyop_2Eieee_2Eroundmode > A_27a] :
      ( ( ( V4f @ c_2Eieee_2ETo__nearest )
        = V0x0 )
      & ( ( V4f @ c_2Eieee_2Efloat__To__zero )
        = V1x1 )
      & ( ( V4f @ c_2Eieee_2ETo__pinfinity )
        = V2x2 )
      & ( ( V4f @ c_2Eieee_2ETo__ninfinity )
        = V3x3 ) ) ).

thf(thm_2Eieee_2Eroundmode__induction,axiom,
    ! [V0P: tyop_2Eieee_2Eroundmode > $o] :
      ( ( ( V0P @ c_2Eieee_2ETo__nearest )
        & ( V0P @ c_2Eieee_2ETo__ninfinity )
        & ( V0P @ c_2Eieee_2ETo__pinfinity )
        & ( V0P @ c_2Eieee_2Efloat__To__zero ) )
     => ! [V1a: tyop_2Eieee_2Eroundmode] : ( V0P @ V1a ) ) ).

thf(thm_2Eieee_2Eroundmode__case__cong,axiom,
    ! [A_27a: $tType,V0v3_27: A_27a,V1v2_27: A_27a,V2v1_27: A_27a,V3v0_27: A_27a,V4M: tyop_2Eieee_2Eroundmode,V5M_27: tyop_2Eieee_2Eroundmode,V6v0: A_27a,V7v1: A_27a,V8v2: A_27a,V9v3: A_27a] :
      ( ( ( V4M = V5M_27 )
        & ( ( V5M_27 = c_2Eieee_2ETo__nearest )
         => ( V6v0 = V3v0_27 ) )
        & ( ( V5M_27 = c_2Eieee_2Efloat__To__zero )
         => ( V7v1 = V2v1_27 ) )
        & ( ( V5M_27 = c_2Eieee_2ETo__pinfinity )
         => ( V8v2 = V1v2_27 ) )
        & ( ( V5M_27 = c_2Eieee_2ETo__ninfinity )
         => ( V9v3 = V0v3_27 ) ) )
     => ( ( c_2Eieee_2Eroundmode__CASE @ A_27a @ V4M @ V6v0 @ V7v1 @ V8v2 @ V9v3 )
        = ( c_2Eieee_2Eroundmode__CASE @ A_27a @ V5M_27 @ V3v0_27 @ V2v1_27 @ V1v2_27 @ V0v3_27 ) ) ) ).

thf(thm_2Eieee_2Eroundmode__case__eq,axiom,
    ! [A_27a: $tType,V0x: tyop_2Eieee_2Eroundmode,V1v3: A_27a,V2v2: A_27a,V3v1: A_27a,V4v0: A_27a,V5v: A_27a] :
      ( ( ( c_2Eieee_2Eroundmode__CASE @ A_27a @ V0x @ V4v0 @ V3v1 @ V2v2 @ V1v3 )
        = V5v )
    <=> ( ( ( V0x = c_2Eieee_2ETo__nearest )
          & ( V4v0 = V5v ) )
        | ( ( V0x = c_2Eieee_2Efloat__To__zero )
          & ( V3v1 = V5v ) )
        | ( ( V0x = c_2Eieee_2ETo__pinfinity )
          & ( V2v2 = V5v ) )
        | ( ( V0x = c_2Eieee_2ETo__ninfinity )
          & ( V1v3 = V5v ) ) ) ) ).

thf(thm_2Eieee_2Enum2ccode__ccode2num,axiom,
    ! [V0a: tyop_2Eieee_2Eccode] :
      ( ( c_2Eieee_2Enum2ccode @ ( c_2Eieee_2Eccode2num @ V0a ) )
      = V0a ) ).

thf(thm_2Eieee_2Eccode2num__num2ccode,axiom,
    ! [V0r: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
    <=> ( ( c_2Eieee_2Eccode2num @ ( c_2Eieee_2Enum2ccode @ V0r ) )
        = V0r ) ) ).

thf(thm_2Eieee_2Enum2ccode__11,axiom,
    ! [V0r: tyop_2Enum_2Enum,V1r_27: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
     => ( ( c_2Eprim__rec_2E_3C @ V1r_27 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       => ( ( ( c_2Eieee_2Enum2ccode @ V0r )
            = ( c_2Eieee_2Enum2ccode @ V1r_27 ) )
        <=> ( V0r = V1r_27 ) ) ) ) ).

thf(thm_2Eieee_2Eccode2num__11,axiom,
    ! [V0a: tyop_2Eieee_2Eccode,V1a_27: tyop_2Eieee_2Eccode] :
      ( ( ( c_2Eieee_2Eccode2num @ V0a )
        = ( c_2Eieee_2Eccode2num @ V1a_27 ) )
    <=> ( V0a = V1a_27 ) ) ).

thf(thm_2Eieee_2Enum2ccode__ONTO,axiom,
    ! [V0a: tyop_2Eieee_2Eccode] :
    ? [V1r: tyop_2Enum_2Enum] :
      ( ( V0a
        = ( c_2Eieee_2Enum2ccode @ V1r ) )
      & ( c_2Eprim__rec_2E_3C @ V1r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2Eieee_2Eccode2num__ONTO,axiom,
    ! [V0r: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ V0r @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
    <=> ? [V1a: tyop_2Eieee_2Eccode] :
          ( V0r
          = ( c_2Eieee_2Eccode2num @ V1a ) ) ) ).

thf(thm_2Eieee_2Enum2ccode__thm,axiom,
    ( ( ( c_2Eieee_2Enum2ccode @ c_2Enum_2E0 )
      = c_2Eieee_2EGt )
    & ( ( c_2Eieee_2Enum2ccode @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Eieee_2ELt )
    & ( ( c_2Eieee_2Enum2ccode @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Eieee_2EEq )
    & ( ( c_2Eieee_2Enum2ccode @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = c_2Eieee_2EUn ) ) ).

thf(thm_2Eieee_2Eccode2num__thm,axiom,
    ( ( ( c_2Eieee_2Eccode2num @ c_2Eieee_2EGt )
      = c_2Enum_2E0 )
    & ( ( c_2Eieee_2Eccode2num @ c_2Eieee_2ELt )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
    & ( ( c_2Eieee_2Eccode2num @ c_2Eieee_2EEq )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
    & ( ( c_2Eieee_2Eccode2num @ c_2Eieee_2EUn )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2Eieee_2Eccode__EQ__ccode,axiom,
    ! [V0a: tyop_2Eieee_2Eccode,V1a_27: tyop_2Eieee_2Eccode] :
      ( ( V0a = V1a_27 )
    <=> ( ( c_2Eieee_2Eccode2num @ V0a )
        = ( c_2Eieee_2Eccode2num @ V1a_27 ) ) ) ).

thf(thm_2Eieee_2Eccode__case__def,axiom,
    ! [A_27a: $tType] :
      ( ! [V0v0: A_27a,V1v1: A_27a,V2v2: A_27a,V3v3: A_27a] :
          ( ( c_2Eieee_2Eccode__CASE @ A_27a @ c_2Eieee_2EGt @ V0v0 @ V1v1 @ V2v2 @ V3v3 )
          = V0v0 )
      & ! [V4v0: A_27a,V5v1: A_27a,V6v2: A_27a,V7v3: A_27a] :
          ( ( c_2Eieee_2Eccode__CASE @ A_27a @ c_2Eieee_2ELt @ V4v0 @ V5v1 @ V6v2 @ V7v3 )
          = V5v1 )
      & ! [V8v0: A_27a,V9v1: A_27a,V10v2: A_27a,V11v3: A_27a] :
          ( ( c_2Eieee_2Eccode__CASE @ A_27a @ c_2Eieee_2EEq @ V8v0 @ V9v1 @ V10v2 @ V11v3 )
          = V10v2 )
      & ! [V12v0: A_27a,V13v1: A_27a,V14v2: A_27a,V15v3: A_27a] :
          ( ( c_2Eieee_2Eccode__CASE @ A_27a @ c_2Eieee_2EUn @ V12v0 @ V13v1 @ V14v2 @ V15v3 )
          = V15v3 ) ) ).

thf(thm_2Eieee_2Edatatype__ccode,axiom,
    ! [V0ccode: tyop_2Eieee_2Eccode > tyop_2Eieee_2Eccode > tyop_2Eieee_2Eccode > tyop_2Eieee_2Eccode > $o] : ( c_2Ebool_2EDATATYPE @ $o @ ( V0ccode @ c_2Eieee_2EGt @ c_2Eieee_2ELt @ c_2Eieee_2EEq @ c_2Eieee_2EUn ) ) ).

thf(thm_2Eieee_2Eccode__distinct,axiom,
    ( ( (~) @ ( c_2Eieee_2EGt = c_2Eieee_2ELt ) )
    & ( (~) @ ( c_2Eieee_2EGt = c_2Eieee_2EEq ) )
    & ( (~) @ ( c_2Eieee_2EGt = c_2Eieee_2EUn ) )
    & ( (~) @ ( c_2Eieee_2ELt = c_2Eieee_2EEq ) )
    & ( (~) @ ( c_2Eieee_2ELt = c_2Eieee_2EUn ) )
    & ( (~) @ ( c_2Eieee_2EEq = c_2Eieee_2EUn ) ) ) ).

thf(thm_2Eieee_2Eccode__nchotomy,axiom,
    ! [V0a: tyop_2Eieee_2Eccode] :
      ( ( V0a = c_2Eieee_2EGt )
      | ( V0a = c_2Eieee_2ELt )
      | ( V0a = c_2Eieee_2EEq )
      | ( V0a = c_2Eieee_2EUn ) ) ).

thf(thm_2Eieee_2Eccode__Axiom,axiom,
    ! [A_27a: $tType,V0x0: A_27a,V1x1: A_27a,V2x2: A_27a,V3x3: A_27a] :
    ? [V4f: tyop_2Eieee_2Eccode > A_27a] :
      ( ( ( V4f @ c_2Eieee_2EGt )
        = V0x0 )
      & ( ( V4f @ c_2Eieee_2ELt )
        = V1x1 )
      & ( ( V4f @ c_2Eieee_2EEq )
        = V2x2 )
      & ( ( V4f @ c_2Eieee_2EUn )
        = V3x3 ) ) ).

thf(thm_2Eieee_2Eccode__induction,axiom,
    ! [V0P: tyop_2Eieee_2Eccode > $o] :
      ( ( ( V0P @ c_2Eieee_2EEq )
        & ( V0P @ c_2Eieee_2EGt )
        & ( V0P @ c_2Eieee_2ELt )
        & ( V0P @ c_2Eieee_2EUn ) )
     => ! [V1a: tyop_2Eieee_2Eccode] : ( V0P @ V1a ) ) ).

thf(thm_2Eieee_2Eccode__case__cong,axiom,
    ! [A_27a: $tType,V0v3_27: A_27a,V1v2_27: A_27a,V2v1_27: A_27a,V3v0_27: A_27a,V4M: tyop_2Eieee_2Eccode,V5M_27: tyop_2Eieee_2Eccode,V6v0: A_27a,V7v1: A_27a,V8v2: A_27a,V9v3: A_27a] :
      ( ( ( V4M = V5M_27 )
        & ( ( V5M_27 = c_2Eieee_2EGt )
         => ( V6v0 = V3v0_27 ) )
        & ( ( V5M_27 = c_2Eieee_2ELt )
         => ( V7v1 = V2v1_27 ) )
        & ( ( V5M_27 = c_2Eieee_2EEq )
         => ( V8v2 = V1v2_27 ) )
        & ( ( V5M_27 = c_2Eieee_2EUn )
         => ( V9v3 = V0v3_27 ) ) )
     => ( ( c_2Eieee_2Eccode__CASE @ A_27a @ V4M @ V6v0 @ V7v1 @ V8v2 @ V9v3 )
        = ( c_2Eieee_2Eccode__CASE @ A_27a @ V5M_27 @ V3v0_27 @ V2v1_27 @ V1v2_27 @ V0v3_27 ) ) ) ).

thf(thm_2Eieee_2Eccode__case__eq,axiom,
    ! [A_27a: $tType,V0x: tyop_2Eieee_2Eccode,V1v3: A_27a,V2v2: A_27a,V3v1: A_27a,V4v0: A_27a,V5v: A_27a] :
      ( ( ( c_2Eieee_2Eccode__CASE @ A_27a @ V0x @ V4v0 @ V3v1 @ V2v2 @ V1v3 )
        = V5v )
    <=> ( ( ( V0x = c_2Eieee_2EGt )
          & ( V4v0 = V5v ) )
        | ( ( V0x = c_2Eieee_2ELt )
          & ( V3v1 = V5v ) )
        | ( ( V0x = c_2Eieee_2EEq )
          & ( V2v2 = V5v ) )
        | ( ( V0x = c_2Eieee_2EUn )
          & ( V1v3 = V5v ) ) ) ) ).

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