ITP001 Axioms: ITP136^7.ax
%------------------------------------------------------------------------------
% File : ITP136^7 : TPTP v8.2.0. 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 ) ) ) ) ).
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