ITP001 Axioms: ITP140_7.ax
%------------------------------------------------------------------------------
% File : ITP140_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 : lift_ieee.ax [Gau19]
% : HL4140_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 280 ( 72 unt; 148 typ; 0 def)
% Number of atoms : 292 ( 112 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 176 ( 16 ~; 3 |; 89 &)
% ( 16 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 122 ( 69 >; 53 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 141 ( 141 usr; 29 con; 0-6 aty)
% Number of variables : 583 ( 425 !; 11 ?; 583 :)
% ( 147 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Ebinary__ieee_2Eflags,type,
tyop_2Ebinary__ieee_2Eflags: $tType ).
tff(tyop_2Ebinary__ieee_2Efloat,type,
tyop_2Ebinary__ieee_2Efloat: ( $tType * $tType ) > $tType ).
tff(tyop_2Ebinary__ieee_2Erounding,type,
tyop_2Ebinary__ieee_2Erounding: $tType ).
tff(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
tff(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: ( $tType * $tType ) > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ereal_2E_2F_2E0,type,
c_2Ereal_2E_2F_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2E_2F_2E2,type,
c_2Ereal_2E_2F_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewords_2EINT__MAX_2E0,type,
c_2Ewords_2EINT__MAX_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Ewords_2EINT__MAX_2E1,type,
c_2Ewords_2EINT__MAX_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).
tff(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Eabs_2E0,type,
c_2Ereal_2Eabs_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Ereal_2Eabs_2E1,type,
c_2Ereal_2Eabs_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Ebinary__ieee_2Eclosest__such_2E0,type,
c_2Ebinary__ieee_2Eclosest__such_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))) ).
tff(c_2Ebinary__ieee_2Eclosest__such_2E3,type,
c_2Ebinary__ieee_2Eclosest__such_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool) * tyop_2Erealax_2Ereal ) > tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b) ) ).
tff(c_2Efcp_2Edimindex_2E0,type,
c_2Efcp_2Edimindex_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Efcp_2Edimindex_2E1,type,
c_2Efcp_2Edimindex_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Elift__ieee_2Eerror_2E0,type,
c_2Elift__ieee_2Eerror_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Elift__ieee_2Eerror_2E2,type,
c_2Elift__ieee_2Eerror_2E2:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)) * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ) ).
tff(c_2Ebinary__ieee_2Efloat__Sign_2E0,type,
c_2Ebinary__ieee_2Efloat__Sign_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)) ).
tff(c_2Ebinary__ieee_2Efloat__Sign_2E1,type,
c_2Ebinary__ieee_2Efloat__Sign_2E1:
!>[A_27t: $tType,A_27w: $tType] : ( tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone) ) ).
tff(c_2Ebinary__ieee_2Efloat__add_2E0,type,
c_2Ebinary__ieee_2Efloat__add_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))) ).
tff(c_2Ebinary__ieee_2Efloat__add_2E3,type,
c_2Ebinary__ieee_2Efloat__add_2E3:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Erounding * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)) ) ).
tff(c_2Ebinary__ieee_2Efloat__div_2E0,type,
c_2Ebinary__ieee_2Efloat__div_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))) ).
tff(c_2Ebinary__ieee_2Efloat__div_2E3,type,
c_2Ebinary__ieee_2Efloat__div_2E3:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Erounding * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)) ) ).
tff(c_2Ebinary__ieee_2Efloat__equal_2E0,type,
c_2Ebinary__ieee_2Efloat__equal_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)) ).
tff(c_2Ebinary__ieee_2Efloat__equal_2E2,type,
c_2Ebinary__ieee_2Efloat__equal_2E2:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebinary__ieee_2Efloat__greater__equal_2E0,type,
c_2Ebinary__ieee_2Efloat__greater__equal_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)) ).
tff(c_2Ebinary__ieee_2Efloat__greater__equal_2E2,type,
c_2Ebinary__ieee_2Efloat__greater__equal_2E2:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebinary__ieee_2Efloat__greater__than_2E0,type,
c_2Ebinary__ieee_2Efloat__greater__than_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)) ).
tff(c_2Ebinary__ieee_2Efloat__greater__than_2E2,type,
c_2Ebinary__ieee_2Efloat__greater__than_2E2:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebinary__ieee_2Efloat__is__finite_2E0,type,
c_2Ebinary__ieee_2Efloat__is__finite_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool) ).
tff(c_2Ebinary__ieee_2Efloat__is__finite_2E1,type,
c_2Ebinary__ieee_2Efloat__is__finite_2E1:
!>[A_27t: $tType,A_27w: $tType] : ( tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebinary__ieee_2Efloat__is__nan_2E0,type,
c_2Ebinary__ieee_2Efloat__is__nan_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool) ).
tff(c_2Ebinary__ieee_2Efloat__is__nan_2E1,type,
c_2Ebinary__ieee_2Efloat__is__nan_2E1:
!>[A_27t: $tType,A_27w: $tType] : ( tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebinary__ieee_2Efloat__is__zero_2E0,type,
c_2Ebinary__ieee_2Efloat__is__zero_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool) ).
tff(c_2Ebinary__ieee_2Efloat__is__zero_2E1,type,
c_2Ebinary__ieee_2Efloat__is__zero_2E1:
!>[A_27t: $tType,A_27w: $tType] : ( tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebinary__ieee_2Efloat__less__equal_2E0,type,
c_2Ebinary__ieee_2Efloat__less__equal_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)) ).
tff(c_2Ebinary__ieee_2Efloat__less__equal_2E2,type,
c_2Ebinary__ieee_2Efloat__less__equal_2E2:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebinary__ieee_2Efloat__less__than_2E0,type,
c_2Ebinary__ieee_2Efloat__less__than_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)) ).
tff(c_2Ebinary__ieee_2Efloat__less__than_2E2,type,
c_2Ebinary__ieee_2Efloat__less__than_2E2:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebinary__ieee_2Efloat__mul_2E0,type,
c_2Ebinary__ieee_2Efloat__mul_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))) ).
tff(c_2Ebinary__ieee_2Efloat__mul_2E3,type,
c_2Ebinary__ieee_2Efloat__mul_2E3:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Erounding * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)) ) ).
tff(c_2Ebinary__ieee_2Efloat__mul__add_2E0,type,
c_2Ebinary__ieee_2Efloat__mul__add_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))) ).
tff(c_2Ebinary__ieee_2Efloat__mul__add_2E4,type,
c_2Ebinary__ieee_2Efloat__mul__add_2E4:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Erounding * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)) ) ).
tff(c_2Ebinary__ieee_2Efloat__mul__sub_2E0,type,
c_2Ebinary__ieee_2Efloat__mul__sub_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))) ).
tff(c_2Ebinary__ieee_2Efloat__mul__sub_2E4,type,
c_2Ebinary__ieee_2Efloat__mul__sub_2E4:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Erounding * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)) ) ).
tff(c_2Ebinary__ieee_2Efloat__round_2E0,type,
c_2Ebinary__ieee_2Efloat__round_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))) ).
tff(c_2Ebinary__ieee_2Efloat__round_2E3,type,
c_2Ebinary__ieee_2Efloat__round_2E3:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Erounding * tyop_2Emin_2Ebool * tyop_2Erealax_2Ereal ) > tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) ).
tff(c_2Ebinary__ieee_2Efloat__sqrt_2E0,type,
c_2Ebinary__ieee_2Efloat__sqrt_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))) ).
tff(c_2Ebinary__ieee_2Efloat__sqrt_2E2,type,
c_2Ebinary__ieee_2Efloat__sqrt_2E2:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Erounding * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)) ) ).
tff(c_2Ebinary__ieee_2Efloat__sub_2E0,type,
c_2Ebinary__ieee_2Efloat__sub_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))) ).
tff(c_2Ebinary__ieee_2Efloat__sub_2E3,type,
c_2Ebinary__ieee_2Efloat__sub_2E3:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Erounding * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) * tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) > tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)) ) ).
tff(c_2Ebinary__ieee_2Efloat__to__real_2E0,type,
c_2Ebinary__ieee_2Efloat__to__real_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Erealax_2Ereal) ).
tff(c_2Ebinary__ieee_2Efloat__to__real_2E1,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1:
!>[A_27t: $tType,A_27w: $tType] : ( tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) > tyop_2Erealax_2Ereal ) ).
tff(c_2Erealax_2Einv_2E0,type,
c_2Erealax_2Einv_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Erealax_2Einv_2E1,type,
c_2Erealax_2Einv_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Ebinary__ieee_2Eis__closest_2E0,type,
c_2Ebinary__ieee_2Eis__closest_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Ebinary__ieee_2Eis__closest_2E3,type,
c_2Ebinary__ieee_2Eis__closest_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool) * tyop_2Erealax_2Ereal * tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebinary__ieee_2Elargest_2E0,type,
c_2Ebinary__ieee_2Elargest_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Erealax_2Ereal) ).
tff(c_2Ebinary__ieee_2Elargest_2E1,type,
c_2Ebinary__ieee_2Elargest_2E1:
!>[A_27t: $tType,A_27w: $tType] : ( tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)) > tyop_2Erealax_2Ereal ) ).
tff(c_2Ewords_2En2w_2E0,type,
c_2Ewords_2En2w_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ewords_2En2w_2E1,type,
c_2Ewords_2En2w_2E1:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Elift__ieee_2Enormalizes_2E0,type,
c_2Elift__ieee_2Enormalizes_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Elift__ieee_2Enormalizes_2E2,type,
c_2Elift__ieee_2Enormalizes_2E2:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)) * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ereal_2Epow_2E0,type,
c_2Ereal_2Epow_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2Epow_2E2,type,
c_2Ereal_2Epow_2E2: ( tyop_2Erealax_2Ereal * tyop_2Enum_2Enum ) > tyop_2Erealax_2Ereal ).
tff(c_2Erealax_2Ereal__add_2E0,type,
c_2Erealax_2Ereal__add_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Erealax_2Ereal__add_2E2,type,
c_2Erealax_2Ereal__add_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__ge_2E0,type,
c_2Ereal_2Ereal__ge_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__ge_2E2,type,
c_2Ereal_2Ereal__ge_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Ereal__gt_2E0,type,
c_2Ereal_2Ereal__gt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__gt_2E2,type,
c_2Ereal_2Ereal__gt_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Erealax_2Ereal__lt_2E0,type,
c_2Erealax_2Ereal__lt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Erealax_2Ereal__lt_2E2,type,
c_2Erealax_2Ereal__lt_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Ereal__lte_2E0,type,
c_2Ereal_2Ereal__lte_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__lte_2E2,type,
c_2Ereal_2Ereal__lte_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Erealax_2Ereal__mul_2E0,type,
c_2Erealax_2Ereal__mul_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Erealax_2Ereal__mul_2E2,type,
c_2Erealax_2Ereal__mul_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Erealax_2Ereal__neg_2E0,type,
c_2Erealax_2Ereal__neg_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Erealax_2Ereal__neg_2E1,type,
c_2Erealax_2Ereal__neg_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__of__num_2E0,type,
c_2Ereal_2Ereal__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) ).
tff(c_2Ereal_2Ereal__of__num_2E1,type,
c_2Ereal_2Ereal__of__num_2E1: tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__sub_2E0,type,
c_2Ereal_2Ereal__sub_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2Ereal__sub_2E2,type,
c_2Ereal_2Ereal__sub_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Ebinary__ieee_2Ereal__to__float_2E0,type,
c_2Ebinary__ieee_2Ereal__to__float_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))) ).
tff(c_2Ebinary__ieee_2Ereal__to__float_2E2,type,
c_2Ebinary__ieee_2Ereal__to__float_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Ebinary__ieee_2Erounding * tyop_2Erealax_2Ereal ) > tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b) ) ).
tff(c_2Ebinary__ieee_2Eround_2E0,type,
c_2Ebinary__ieee_2Eround_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))) ).
tff(c_2Ebinary__ieee_2Eround_2E2,type,
c_2Ebinary__ieee_2Eround_2E2:
!>[A_27t: $tType,A_27w: $tType] : ( ( tyop_2Ebinary__ieee_2Erounding * tyop_2Erealax_2Ereal ) > tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w) ) ).
tff(c_2Ebinary__ieee_2EroundTiesToEven_2E0,type,
c_2Ebinary__ieee_2EroundTiesToEven_2E0: tyop_2Ebinary__ieee_2Erounding ).
tff(c_2Etransc_2Esqrt_2E0,type,
c_2Etransc_2Esqrt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Etransc_2Esqrt_2E1,type,
c_2Etransc_2Esqrt_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Ebool_2Ethe__value_2E0,type,
c_2Ebool_2Ethe__value_2E0:
!>[A_27a: $tType] : tyop_2Ebool_2Eitself(A_27a) ).
tff(c_2Ebinary__ieee_2Ethreshold_2E0,type,
c_2Ebinary__ieee_2Ethreshold_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Erealax_2Ereal) ).
tff(c_2Ebinary__ieee_2Ethreshold_2E1,type,
c_2Ebinary__ieee_2Ethreshold_2E1:
!>[A_27t: $tType,A_27w: $tType] : ( tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)) > tyop_2Erealax_2Ereal ) ).
tff(c_2Ebinary__ieee_2Eulp_2E0,type,
c_2Ebinary__ieee_2Eulp_2E0:
!>[A_27t: $tType,A_27w: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Erealax_2Ereal) ).
tff(c_2Ebinary__ieee_2Eulp_2E1,type,
c_2Ebinary__ieee_2Eulp_2E1:
!>[A_27t: $tType,A_27w: $tType] : ( tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)) > tyop_2Erealax_2Ereal ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2E_2F_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2E_2F_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2E_2F_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2EINT__MAX_2E1_2Emono_2EA_27w,axiom,
! [A_27w: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27w)] : ( c_2Ewords_2EINT__MAX_2E1(A_27w,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27w),tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E0(A_27w),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))] : ( c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Epair_2ESND_2E0(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ereal_2Eabs_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Eabs_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebinary__ieee_2Eclosest__such_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X2_2E0: tyop_2Erealax_2Ereal] : ( c_2Ebinary__ieee_2Eclosest__such_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Eclosest__such_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27t,axiom,
! [A_27t: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27t)] : ( c_2Efcp_2Edimindex_2E1(A_27t,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27t),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(A_27t),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elift__ieee_2Eerror_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Elift__ieee_2Eerror_2E0(A_27t,A_27w),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__Sign_2E1(A_27t,A_27w,X0_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E0(A_27t,A_27w),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__add_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__add_2E3(A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebinary__ieee_2Efloat__add_2E0(A_27t,A_27w),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__div_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__div_2E3(A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebinary__ieee_2Efloat__div_2E0(A_27t,A_27w),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ebinary__ieee_2Efloat__equal_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( c_2Ebinary__ieee_2Efloat__equal_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__equal_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebinary__ieee_2Efloat__greater__equal_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( c_2Ebinary__ieee_2Efloat__greater__equal_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__greater__equal_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebinary__ieee_2Efloat__greater__than_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( c_2Ebinary__ieee_2Efloat__greater__than_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__greater__than_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__finite_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__finite_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,X0_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E0(A_27t,A_27w),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__nan_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( c_2Ebinary__ieee_2Efloat__is__nan_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__zero_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( c_2Ebinary__ieee_2Efloat__is__zero_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__is__zero_2E1(A_27t,A_27w,X0_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E0(A_27t,A_27w),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebinary__ieee_2Efloat__less__equal_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( c_2Ebinary__ieee_2Efloat__less__equal_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__less__equal_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebinary__ieee_2Efloat__less__than_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( c_2Ebinary__ieee_2Efloat__less__than_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__less__than_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__mul_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__mul_2E3(A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebinary__ieee_2Efloat__mul_2E0(A_27t,A_27w),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__add_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__mul__add_2E4(A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebinary__ieee_2Efloat__mul__add_2E0(A_27t,A_27w),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__sub_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__mul__sub_2E4(A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebinary__ieee_2Efloat__mul__sub_2E0(A_27t,A_27w),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Erealax_2Ereal] : ( c_2Ebinary__ieee_2Efloat__round_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Efloat__round_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Erealax_2Ereal] : ( c_2Ebinary__ieee_2Efloat__round_2E3(A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebinary__ieee_2Efloat__round_2E0(A_27t,A_27w),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ebinary__ieee_2Efloat__sqrt_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__sqrt_2E2(A_27t,A_27w,X0_2E0,X1_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebinary__ieee_2Efloat__sqrt_2E0(A_27t,A_27w),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__sub_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__sub_2E3(A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebinary__ieee_2Efloat__sub_2E0(A_27t,A_27w),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,X0_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(A_27t,A_27w),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erealax_2Einv_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Einv_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Einv_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebinary__ieee_2Eis__closest_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Erealax_2Ereal,X2_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( c_2Ebinary__ieee_2Eis__closest_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Ebinary__ieee_2Eis__closest_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Elargest_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w))] : ( c_2Ebinary__ieee_2Elargest_2E1(A_27t,A_27w,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E0(A_27t,A_27w),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elift__ieee_2Enormalizes_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Elift__ieee_2Enormalizes_2E2(A_27t,A_27w,X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Elift__ieee_2Enormalizes_2E0(A_27t,A_27w),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Epow_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Epow_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),c_2Ereal_2Epow_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__add_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__ge_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__ge_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__ge_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__gt_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__gt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__gt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Erealax_2Ereal__lt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__lte_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__mul_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erealax_2Ereal__neg_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__neg_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Ereal__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__sub_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2Ereal__sub_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebinary__ieee_2Ereal__to__float_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ebinary__ieee_2Ereal__to__float_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Ereal__to__float_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebinary__ieee_2Eround_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ebinary__ieee_2Eround_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Eround_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebinary__ieee_2Eround_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebinary__ieee_2Erounding,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ebinary__ieee_2Eround_2E2(A_27t,A_27w,X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Eround_2E0(A_27t,A_27w),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Etransc_2Esqrt_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Etransc_2Esqrt_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Etransc_2Esqrt_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Ethreshold_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ebinary__ieee_2Ethreshold_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Ethreshold_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: $tType,A_27w: $tType,X0_2E0: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w))] : ( c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E0(A_27t,A_27w),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ebinary__ieee_2Eulp_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Elift__ieee_2Eerror__def,axiom,
! [A_27t: $tType,A_27w: $tType,V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),V0x_2E0) = c_2Ereal_2Ereal__sub_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Ebinary__ieee_2Eround_2E2(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0x_2E0)),V0x_2E0) ) ).
tff(thm_2Elift__ieee_2Enormalizes__def,axiom,
! [A_27t: $tType,A_27w: $tType,V0x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Elift__ieee_2Enormalizes_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),V0x_2E0))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Ewords_2EINT__MAX_2E1(A_27w,c_2Ebool_2Ethe__value_2E0(A_27w))))
& p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Einv_2E1(c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2D_2E2(c_2Ewords_2EINT__MAX_2E1(A_27w,c_2Ebool_2Ethe__value_2E0(A_27w)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ereal_2Eabs_2E1(V0x_2E0)))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(V0x_2E0),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) ) ) ).
tff(thm_2Elift__ieee_2Efloat__lt,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V0x_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V1y_2E0)) )
=> ( c_2Ebinary__ieee_2Efloat__less__than_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0) = c_2Erealax_2Ereal__lt_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V0x_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V1y_2E0)) ) ) ).
tff(thm_2Elift__ieee_2Efloat__le,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V0x_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V1y_2E0)) )
=> ( c_2Ebinary__ieee_2Efloat__less__equal_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0) = c_2Ereal_2Ereal__lte_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V0x_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V1y_2E0)) ) ) ).
tff(thm_2Elift__ieee_2Efloat__gt,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V0x_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V1y_2E0)) )
=> ( c_2Ebinary__ieee_2Efloat__greater__than_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0) = c_2Ereal_2Ereal__gt_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V0x_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V1y_2E0)) ) ) ).
tff(thm_2Elift__ieee_2Efloat__ge,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V0x_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V1y_2E0)) )
=> ( c_2Ebinary__ieee_2Efloat__greater__equal_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0) = c_2Ereal_2Ereal__ge_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V0x_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V1y_2E0)) ) ) ).
tff(thm_2Elift__ieee_2Efloat__eq,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V0x_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V1y_2E0)) )
=> ( p(c_2Ebinary__ieee_2Efloat__equal_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0))
<=> ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V0x_2E0) = c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V1y_2E0) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__eq__refl,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] :
( p(c_2Ebinary__ieee_2Efloat__equal_2E2(A_27a,A_27b,V0x_2E0,V0x_2E0))
<=> ~ p(c_2Ebinary__ieee_2Efloat__is__nan_2E1(A_27a,A_27b,V0x_2E0)) ) ).
tff(thm_2Elift__ieee_2Eis__closest__exits,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Erealax_2Ereal,V1s_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1s_2E0))
=> ( ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)) )
=> ? [V2a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : p(c_2Ebinary__ieee_2Eis__closest_2E3(A_27a,A_27b,V1s_2E0,V0x_2E0,V2a_2E0)) ) ) ).
tff(thm_2Elift__ieee_2Eclosest__is__everything,axiom,
! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V2x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1s_2E0))
=> ( ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)) )
=> ( p(c_2Ebinary__ieee_2Eis__closest_2E3(A_27a,A_27b,V1s_2E0,V2x_2E0,c_2Ebinary__ieee_2Eclosest__such_2E3(A_27a,A_27b,V0p_2E0,V1s_2E0,V2x_2E0)))
& ( ? [V3b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] :
( p(c_2Ebinary__ieee_2Eis__closest_2E3(A_27a,A_27b,V1s_2E0,V2x_2E0,V3b_2E0))
& p(app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,V0p_2E0,V3b_2E0)) )
=> p(app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,V0p_2E0,c_2Ebinary__ieee_2Eclosest__such_2E3(A_27a,A_27b,V0p_2E0,V1s_2E0,V2x_2E0))) ) ) ) ) ).
tff(thm_2Elift__ieee_2Eclosest__in__set,axiom,
! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V2x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1s_2E0))
=> ( ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)) )
=> p(c_2Ebool_2EIN_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Eclosest__such_2E3(A_27a,A_27b,V0p_2E0,V1s_2E0,V2x_2E0),V1s_2E0)) ) ) ).
tff(thm_2Elift__ieee_2Eclosest__is__closest,axiom,
! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V2x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1s_2E0))
=> ( ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)) )
=> p(c_2Ebinary__ieee_2Eis__closest_2E3(A_27a,A_27b,V1s_2E0,V2x_2E0,c_2Ebinary__ieee_2Eclosest__such_2E3(A_27a,A_27b,V0p_2E0,V1s_2E0,V2x_2E0))) ) ) ).
tff(thm_2Elift__ieee_2Efloat__finite,axiom,
! [A_27t: $tType,A_27w: $tType] : p(c_2Epred__set_2EFINITE_2E1(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Epred__set_2EUNIV_2E0(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))) ).
tff(thm_2Elift__ieee_2Eis__finite__finite,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))] :
( ! [V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),F0_2E0,V0a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,V0a_2E0,c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V0a_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Epred__set_2EGSPEC_2E1(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),F0_2E0))) ) ).
tff(thm_2Elift__ieee_2Eis__finite__nonempty,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))] :
( ! [V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),F0_2E0,V0a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,V0a_2E0,c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V0a_2E0)) )
=> ( c_2Epred__set_2EGSPEC_2E1(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),F0_2E0) != c_2Epred__set_2EEMPTY_2E0(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)) ) ) ).
tff(thm_2Elift__ieee_2Eis__finite__closest,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))] :
( ! [V2a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] : ( app_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),F0_2E0,V2a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool,V2a_2E0,c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V2a_2E0)) )
=> ! [V0p_2E0: tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1x_2E0: tyop_2Erealax_2Ereal] : p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,c_2Ebinary__ieee_2Eclosest__such_2E3(A_27a,A_27b,V0p_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),F0_2E0),V1x_2E0))) ) ).
tff(thm_2Elift__ieee_2Efloat__to__real__finite,axiom,
! [A_27t: $tType,A_27w: $tType,V0x_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0x_2E0))
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0x_2E0)),c_2Ebinary__ieee_2Elargest_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) ) ).
tff(thm_2Elift__ieee_2Efloat__to__real__threshold,axiom,
! [A_27t: $tType,A_27w: $tType,V0x_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0x_2E0))
=> p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0x_2E0)),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) ) ).
tff(thm_2Elift__ieee_2Eerror__at__worst__lemma,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0: tyop_2Erealax_2Ereal] :
( ( p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(V1x_2E0),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)))))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0)) )
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),V1x_2E0)),c_2Ereal_2Eabs_2E1(c_2Ereal_2Ereal__sub_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),V1x_2E0)))) ) ).
tff(thm_2Elift__ieee_2Eerror__is__zero,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0: tyop_2Erealax_2Ereal] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0) = V1x_2E0 ) )
=> ( c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),V1x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2Elift__ieee_2Erelative__error,axiom,
! [A_27t: $tType,A_27w: $tType,V0x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Elift__ieee_2Enormalizes_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),V0x_2E0))
=> ? [V1e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V1e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(c_2Efcp_2Edimindex_2E1(A_27t,c_2Ebool_2Ethe__value_2E0(A_27t)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Ebinary__ieee_2Eround_2E2(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0x_2E0)) = c_2Erealax_2Ereal__mul_2E2(V0x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1e_2E0)) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__round__finite,axiom,
! [A_27t: $tType,A_27w: $tType,V0b_2E0: tyop_2Emin_2Ebool,V1x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(V1x_2E0),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)))))
=> p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Ebinary__ieee_2Efloat__round_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0b_2E0,V1x_2E0))) ) ).
tff(thm_2Elift__ieee_2Efloat__add,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Erealax_2Ereal__add_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__add_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__add_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__add_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Erealax_2Ereal__add_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)))) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__sub,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Ereal_2Ereal__sub_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__sub_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__sub_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))) = c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__sub_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ereal_2Ereal__sub_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)))) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__mul,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)))) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__div,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& ~ p(c_2Ebinary__ieee_2Efloat__is__zero_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Ereal_2E_2F_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__div_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__div_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))) = c_2Erealax_2Ereal__add_2E2(c_2Ereal_2E_2F_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ereal_2E_2F_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)))) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__sqrt,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& ( c_2Ebinary__ieee_2Efloat__Sign_2E1(A_27t,A_27w,V0a_2E0) = c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Enum_2E0_2E0) )
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Etransc_2Esqrt_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__sqrt_2E2(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__sqrt_2E2(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0))) = c_2Erealax_2Ereal__add_2E2(c_2Etransc_2Esqrt_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0)),c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Etransc_2Esqrt_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0)))) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__mul__add,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V2c_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul__add_2E4(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0,V2c_2E0))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul__add_2E4(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0,V2c_2E0))) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0)),c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0)))) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__mul__sub,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V2c_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul__sub_2E4(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0,V2c_2E0))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul__sub_2E4(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0,V2c_2E0))) = c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0)),c_2Elift__ieee_2Eerror_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0)))) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__add__finite,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Erealax_2Ereal__add_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__add_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0)))) ) ).
tff(thm_2Elift__ieee_2Efloat__sub__finite,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Ereal_2Ereal__sub_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__sub_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0)))) ) ).
tff(thm_2Elift__ieee_2Efloat__mul__finite,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0)))) ) ).
tff(thm_2Elift__ieee_2Efloat__div__finite,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& ~ p(c_2Ebinary__ieee_2Efloat__is__zero_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Ereal_2E_2F_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__div_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0)))) ) ).
tff(thm_2Elift__ieee_2Efloat__sqrt__finite,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& ( c_2Ebinary__ieee_2Efloat__Sign_2E1(A_27t,A_27w,V0a_2E0) = c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Enum_2E0_2E0) )
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Etransc_2Esqrt_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__sqrt_2E2(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0)))) ) ).
tff(thm_2Elift__ieee_2Efloat__mul__add__finite,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V2c_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul__add_2E4(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0,V2c_2E0)))) ) ).
tff(thm_2Elift__ieee_2Efloat__mul__sub__finite,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V2c_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0))),c_2Ebinary__ieee_2Ethreshold_2E1(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul__sub_2E4(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0,V2c_2E0)))) ) ).
tff(thm_2Elift__ieee_2Efloat__add__relative,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Elift__ieee_2Enormalizes_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Erealax_2Ereal__add_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__add_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))))
& ? [V2e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V2e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(c_2Efcp_2Edimindex_2E1(A_27t,c_2Ebool_2Ethe__value_2E0(A_27t)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__add_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))) = c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__add_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__sub__relative,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Elift__ieee_2Enormalizes_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ereal_2Ereal__sub_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__sub_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))))
& ? [V2e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V2e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(c_2Efcp_2Edimindex_2E1(A_27t,c_2Ebool_2Ethe__value_2E0(A_27t)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__sub_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__sub_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__mul__relative,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Elift__ieee_2Enormalizes_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))))
& ? [V2e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V2e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(c_2Efcp_2Edimindex_2E1(A_27t,c_2Ebool_2Ethe__value_2E0(A_27t)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))) = c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__div__relative,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& ~ p(c_2Ebinary__ieee_2Efloat__is__zero_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Elift__ieee_2Enormalizes_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ereal_2E_2F_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__div_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))))
& ? [V2e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V2e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(c_2Efcp_2Edimindex_2E1(A_27t,c_2Ebool_2Ethe__value_2E0(A_27t)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__div_2E3(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0))) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2E_2F_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__sqrt__relative,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& ( c_2Ebinary__ieee_2Efloat__Sign_2E1(A_27t,A_27w,V0a_2E0) = c_2Ewords_2En2w_2E1(tyop_2Eone_2Eone,c_2Enum_2E0_2E0) )
& p(c_2Elift__ieee_2Enormalizes_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Etransc_2Esqrt_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0)))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__sqrt_2E2(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0))))
& ? [V1e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V1e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(c_2Efcp_2Edimindex_2E1(A_27t,c_2Ebool_2Ethe__value_2E0(A_27t)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__sqrt_2E2(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0))) = c_2Erealax_2Ereal__mul_2E2(c_2Etransc_2Esqrt_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1e_2E0)) ) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__mul__add__relative,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V2c_2E0))
& p(c_2Elift__ieee_2Enormalizes_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0)))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul__add_2E4(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0,V2c_2E0))))
& ? [V3e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V3e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(c_2Efcp_2Edimindex_2E1(A_27t,c_2Ebool_2Ethe__value_2E0(A_27t)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul__add_2E4(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0,V2c_2E0))) = c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V3e_2E0)) ) ) ) ) ).
tff(thm_2Elift__ieee_2Efloat__mul__sub__relative,axiom,
! [A_27t: $tType,A_27w: $tType,V0a_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0: tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V0a_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V1b_2E0))
& p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,V2c_2E0))
& p(c_2Elift__ieee_2Enormalizes_2E2(A_27t,A_27w,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0)))) )
=> ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul__sub_2E4(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0,V2c_2E0))))
& ? [V3e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V3e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(c_2Efcp_2Edimindex_2E1(A_27t,c_2Ebool_2Ethe__value_2E0(A_27t)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
& ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,c_2Epair_2ESND_2E1(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__mul__sub_2E4(A_27t,A_27w,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V0a_2E0,V1b_2E0,V2c_2E0))) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__sub_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V0a_2E0),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V1b_2E0)),c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27t,A_27w,V2c_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V3e_2E0)) ) ) ) ) ).
tff(thm_2Elift__ieee_2Efinite__float__within__threshold,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] :
( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V0f_2E0))
=> ( ~ p(c_2Ereal_2Ereal__lte_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V0f_2E0),c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Ethreshold_2E1(A_27a,A_27b,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))))
& ~ p(c_2Ereal_2Ereal__ge_2E2(c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V0f_2E0),c_2Ebinary__ieee_2Ethreshold_2E1(A_27a,A_27b,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))) ) ) ).
tff(thm_2Elift__ieee_2Eround__finite__normal__float__id,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V0f_2E0))
& ~ p(c_2Ebinary__ieee_2Efloat__is__zero_2E1(A_27a,A_27b,V0f_2E0)) )
=> ( c_2Ebinary__ieee_2Eround_2E2(A_27a,A_27b,c_2Ebinary__ieee_2EroundTiesToEven_2E0,c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V0f_2E0)) = V0f_2E0 ) ) ).
tff(thm_2Elift__ieee_2Ereal__to__float__finite__normal__id,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)] :
( ( p(c_2Ebinary__ieee_2Efloat__is__finite_2E1(A_27a,A_27b,V0f_2E0))
& ~ p(c_2Ebinary__ieee_2Efloat__is__zero_2E1(A_27a,A_27b,V0f_2E0)) )
=> ( c_2Ebinary__ieee_2Ereal__to__float_2E2(A_27a,A_27b,c_2Ebinary__ieee_2EroundTiesToEven_2E0,c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,V0f_2E0)) = V0f_2E0 ) ) ).
tff(thm_2Elift__ieee_2Efloat__to__real__real__to__float__zero__id,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,c_2Ebinary__ieee_2Ereal__to__float_2E2(A_27a,A_27b,c_2Ebinary__ieee_2EroundTiesToEven_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0))) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ).
tff(thm_2Elift__ieee_2Enon__representable__float__is__zero,axiom,
! [A_27a: $tType,A_27b: $tType,V0ff_2E0: tyop_2Erealax_2Ereal,V1P_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Eabs_2E1(V0ff_2E0)),c_2Ebinary__ieee_2Eulp_2E1(A_27a,A_27b,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)))))
=> ( c_2Ebinary__ieee_2Efloat__to__real_2E1(A_27a,A_27b,c_2Ebinary__ieee_2Efloat__round_2E3(A_27a,A_27b,c_2Ebinary__ieee_2EroundTiesToEven_2E0,V1P_2E0,V0ff_2E0)) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
%------------------------------------------------------------------------------