ITP001 Axioms: ITP145^7.ax
%------------------------------------------------------------------------------
% File : ITP145^7 : 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_machine_ieee.ax [Gau19]
% : HL4145^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 95 ( 6 unt; 66 typ; 0 def)
% Number of atoms : 177 ( 23 equ; 7 cnn)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 3508 ( 7 ~; 1 |; 94 &;3377 @)
% ( 7 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 17 avg;3377 nst)
% Number of types : 6 ( 5 usr)
% Number of type conns : 129 ( 129 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 61 usr; 3 con; 0-4 aty)
% Number of variables : 94 ( 1 ^ 62 !; 22 ?; 94 :)
% ( 9 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Ebinary__ieee_2Erounding,type,
tyop_2Ebinary__ieee_2Erounding: $tType ).
thf(tyop_2Efcp_2Ebit0,type,
tyop_2Efcp_2Ebit0: $tType > $tType ).
thf(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: $tType > $tType > $tType ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Epair_2E_2C,type,
c_2Epair_2E_2C:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).
thf(c_2Ereal_2E_2F,type,
c_2Ereal_2E_2F: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EBIT2,type,
c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Epred__set_2EGSPEC,type,
c_2Epred__set_2EGSPEC:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27b > ( tyop_2Epair_2Eprod @ A_27a @ $o ) ) > A_27a > $o ) ).
thf(c_2Ebool_2EIN,type,
c_2Ebool_2EIN:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ereal_2Eabs,type,
c_2Ereal_2Eabs: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Emachine__ieee_2Efp16__add,type,
c_2Emachine__ieee_2Efp16__add: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp16__div,type,
c_2Emachine__ieee_2Efp16__div: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp16__isFinite,type,
c_2Emachine__ieee_2Efp16__isFinite: ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > $o ).
thf(c_2Emachine__ieee_2Efp16__isZero,type,
c_2Emachine__ieee_2Efp16__isZero: ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > $o ).
thf(c_2Emachine__ieee_2Efp16__mul,type,
c_2Emachine__ieee_2Efp16__mul: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp16__mul__add,type,
c_2Emachine__ieee_2Efp16__mul__add: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp16__mul__sub,type,
c_2Emachine__ieee_2Efp16__mul__sub: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp16__sqrt,type,
c_2Emachine__ieee_2Efp16__sqrt: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp16__sub,type,
c_2Emachine__ieee_2Efp16__sub: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp16__to__real,type,
c_2Emachine__ieee_2Efp16__to__real: ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) > tyop_2Erealax_2Ereal ).
thf(c_2Emachine__ieee_2Efp32__add,type,
c_2Emachine__ieee_2Efp32__add: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp32__div,type,
c_2Emachine__ieee_2Efp32__div: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp32__isFinite,type,
c_2Emachine__ieee_2Efp32__isFinite: ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > $o ).
thf(c_2Emachine__ieee_2Efp32__isZero,type,
c_2Emachine__ieee_2Efp32__isZero: ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > $o ).
thf(c_2Emachine__ieee_2Efp32__mul,type,
c_2Emachine__ieee_2Efp32__mul: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp32__mul__add,type,
c_2Emachine__ieee_2Efp32__mul__add: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp32__mul__sub,type,
c_2Emachine__ieee_2Efp32__mul__sub: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp32__sqrt,type,
c_2Emachine__ieee_2Efp32__sqrt: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp32__sub,type,
c_2Emachine__ieee_2Efp32__sub: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp32__to__real,type,
c_2Emachine__ieee_2Efp32__to__real: ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) > tyop_2Erealax_2Ereal ).
thf(c_2Emachine__ieee_2Efp64__add,type,
c_2Emachine__ieee_2Efp64__add: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp64__div,type,
c_2Emachine__ieee_2Efp64__div: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp64__isFinite,type,
c_2Emachine__ieee_2Efp64__isFinite: ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > $o ).
thf(c_2Emachine__ieee_2Efp64__isZero,type,
c_2Emachine__ieee_2Efp64__isZero: ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > $o ).
thf(c_2Emachine__ieee_2Efp64__mul,type,
c_2Emachine__ieee_2Efp64__mul: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp64__mul__add,type,
c_2Emachine__ieee_2Efp64__mul__add: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp64__mul__sub,type,
c_2Emachine__ieee_2Efp64__mul__sub: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp64__sqrt,type,
c_2Emachine__ieee_2Efp64__sqrt: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp64__sub,type,
c_2Emachine__ieee_2Efp64__sub: tyop_2Ebinary__ieee_2Erounding > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(c_2Emachine__ieee_2Efp64__to__real,type,
c_2Emachine__ieee_2Efp64__to__real: ( tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) > tyop_2Erealax_2Ereal ).
thf(c_2Elift__machine__ieee_2Einterval,type,
c_2Elift__machine__ieee_2Einterval: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).
thf(c_2Ereal_2Epow,type,
c_2Ereal_2Epow: tyop_2Erealax_2Ereal > tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).
thf(c_2Erealax_2Ereal__add,type,
c_2Erealax_2Ereal__add: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Erealax_2Ereal__lt,type,
c_2Erealax_2Ereal__lt: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).
thf(c_2Ereal_2Ereal__lte,type,
c_2Ereal_2Ereal__lte: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).
thf(c_2Erealax_2Ereal__mul,type,
c_2Erealax_2Ereal__mul: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ereal_2Ereal__of__num,type,
c_2Ereal_2Ereal__of__num: tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).
thf(c_2Ereal_2Ereal__sub,type,
c_2Ereal_2Ereal__sub: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ebinary__ieee_2EroundTiesToEven,type,
c_2Ebinary__ieee_2EroundTiesToEven: tyop_2Ebinary__ieee_2Erounding ).
thf(c_2Etransc_2Esqrt,type,
c_2Etransc_2Esqrt: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ewords_2Eword__msb,type,
c_2Ewords_2Eword__msb:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2Elift__machine__ieee_2Einterval__def,axiom,
! [V0a: tyop_2Erealax_2Ereal,V1b: tyop_2Erealax_2Ereal] :
( ( c_2Elift__machine__ieee_2Einterval @ V0a @ V1b )
= ( c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal
@ ^ [V2x: tyop_2Erealax_2Ereal] : ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ V2x @ ( c_2Ebool_2E_2F_5C @ ( c_2Ereal_2Ereal__lte @ V0a @ V2x ) @ ( c_2Erealax_2Ereal__lt @ V2x @ V1b ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp16__float__add__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp16__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp16__isFinite @ V1b )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Erealax_2Ereal__add @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp16__isFinite @ ( c_2Emachine__ieee_2Efp16__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp16__to__real @ ( c_2Emachine__ieee_2Efp16__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__add @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp16__float__sub__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp16__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp16__isFinite @ V1b )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2Ereal__sub @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp16__isFinite @ ( c_2Emachine__ieee_2Efp16__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp16__to__real @ ( c_2Emachine__ieee_2Efp16__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__sub @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp16__float__mul__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp16__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp16__isFinite @ V1b )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp16__isFinite @ ( c_2Emachine__ieee_2Efp16__mul @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp16__to__real @ ( c_2Emachine__ieee_2Efp16__mul @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp16__float__mul__add__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ),V2c: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp16__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp16__isFinite @ V1b )
& ( c_2Emachine__ieee_2Efp16__isFinite @ V2c )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V2c ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp16__isFinite @ ( c_2Emachine__ieee_2Efp16__mul__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
& ? [V3e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V3e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp16__to__real @ ( c_2Emachine__ieee_2Efp16__mul__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V2c ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V3e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp16__float__mul__sub__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ),V2c: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp16__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp16__isFinite @ V1b )
& ( c_2Emachine__ieee_2Efp16__isFinite @ V2c )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V2c ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp16__isFinite @ ( c_2Emachine__ieee_2Efp16__mul__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
& ? [V3e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V3e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp16__to__real @ ( c_2Emachine__ieee_2Efp16__mul__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V2c ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V3e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp16__float__div__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp16__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp16__isFinite @ V1b )
& ( (~) @ ( c_2Emachine__ieee_2Efp16__isZero @ V1b ) )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2E_2F @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp16__isFinite @ ( c_2Emachine__ieee_2Efp16__div @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp16__to__real @ ( c_2Emachine__ieee_2Efp16__div @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp16__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp16__float__sqrt__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp16__isFinite @ V0a )
& ( (~) @ ( c_2Ewords_2Eword__msb @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ V0a ) )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Etransc_2Esqrt @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp16__isFinite @ ( c_2Emachine__ieee_2Efp16__sqrt @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a ) )
& ? [V1e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V1e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp16__to__real @ ( c_2Emachine__ieee_2Efp16__sqrt @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Etransc_2Esqrt @ ( c_2Emachine__ieee_2Efp16__to__real @ V0a ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp32__float__add__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp32__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp32__isFinite @ V1b )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Erealax_2Ereal__add @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp32__isFinite @ ( c_2Emachine__ieee_2Efp32__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp32__to__real @ ( c_2Emachine__ieee_2Efp32__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__add @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp32__float__sub__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp32__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp32__isFinite @ V1b )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2Ereal__sub @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp32__isFinite @ ( c_2Emachine__ieee_2Efp32__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp32__to__real @ ( c_2Emachine__ieee_2Efp32__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__sub @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp32__float__mul__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp32__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp32__isFinite @ V1b )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp32__isFinite @ ( c_2Emachine__ieee_2Efp32__mul @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp32__to__real @ ( c_2Emachine__ieee_2Efp32__mul @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp32__float__mul__add__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ),V2c: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp32__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp32__isFinite @ V1b )
& ( c_2Emachine__ieee_2Efp32__isFinite @ V2c )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V2c ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp32__isFinite @ ( c_2Emachine__ieee_2Efp32__mul__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
& ? [V3e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V3e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp32__to__real @ ( c_2Emachine__ieee_2Efp32__mul__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V2c ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V3e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp32__float__mul__sub__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ),V2c: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp32__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp32__isFinite @ V1b )
& ( c_2Emachine__ieee_2Efp32__isFinite @ V2c )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V2c ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp32__isFinite @ ( c_2Emachine__ieee_2Efp32__mul__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
& ? [V3e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V3e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp32__to__real @ ( c_2Emachine__ieee_2Efp32__mul__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V2c ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V3e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp32__float__div__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp32__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp32__isFinite @ V1b )
& ( (~) @ ( c_2Emachine__ieee_2Efp32__isZero @ V1b ) )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2E_2F @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp32__isFinite @ ( c_2Emachine__ieee_2Efp32__div @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp32__to__real @ ( c_2Emachine__ieee_2Efp32__div @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp32__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp32__float__sqrt__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp32__isFinite @ V0a )
& ( (~) @ ( c_2Ewords_2Eword__msb @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ V0a ) )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Etransc_2Esqrt @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp32__isFinite @ ( c_2Emachine__ieee_2Efp32__sqrt @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a ) )
& ? [V1e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V1e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp32__to__real @ ( c_2Emachine__ieee_2Efp32__sqrt @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Etransc_2Esqrt @ ( c_2Emachine__ieee_2Efp32__to__real @ V0a ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp64__float__add__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp64__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp64__isFinite @ V1b )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Erealax_2Ereal__add @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp64__isFinite @ ( c_2Emachine__ieee_2Efp64__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp64__to__real @ ( c_2Emachine__ieee_2Efp64__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__add @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp64__float__sub__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp64__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp64__isFinite @ V1b )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2Ereal__sub @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp64__isFinite @ ( c_2Emachine__ieee_2Efp64__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp64__to__real @ ( c_2Emachine__ieee_2Efp64__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__sub @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp64__float__mul__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp64__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp64__isFinite @ V1b )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp64__isFinite @ ( c_2Emachine__ieee_2Efp64__mul @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp64__to__real @ ( c_2Emachine__ieee_2Efp64__mul @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp64__float__mul__add__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ),V2c: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp64__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp64__isFinite @ V1b )
& ( c_2Emachine__ieee_2Efp64__isFinite @ V2c )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V2c ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp64__isFinite @ ( c_2Emachine__ieee_2Efp64__mul__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
& ? [V3e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V3e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp64__to__real @ ( c_2Emachine__ieee_2Efp64__mul__add @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V2c ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V3e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp64__float__mul__sub__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ),V2c: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp64__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp64__isFinite @ V1b )
& ( c_2Emachine__ieee_2Efp64__isFinite @ V2c )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V2c ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp64__isFinite @ ( c_2Emachine__ieee_2Efp64__mul__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
& ? [V3e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V3e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp64__to__real @ ( c_2Emachine__ieee_2Efp64__mul__sub @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b @ V2c ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__mul @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V2c ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V3e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp64__float__div__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ),V1b: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp64__isFinite @ V0a )
& ( c_2Emachine__ieee_2Efp64__isFinite @ V1b )
& ( (~) @ ( c_2Emachine__ieee_2Efp64__isZero @ V1b ) )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Ereal_2E_2F @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp64__isFinite @ ( c_2Emachine__ieee_2Efp64__div @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
& ? [V2e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V2e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp64__to__real @ ( c_2Emachine__ieee_2Efp64__div @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a @ V1b ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) @ ( c_2Emachine__ieee_2Efp64__to__real @ V1b ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__machine__ieee_2Efp64__float__sqrt__relative,axiom,
! [V0a: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) )] :
( ( ( c_2Emachine__ieee_2Efp64__isFinite @ V0a )
& ( (~) @ ( c_2Ewords_2Eword__msb @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) @ V0a ) )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ ( c_2Ereal_2Eabs @ ( c_2Etransc_2Esqrt @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) ) ) @ ( c_2Elift__machine__ieee_2Einterval @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( ( c_2Emachine__ieee_2Efp64__isFinite @ ( c_2Emachine__ieee_2Efp64__sqrt @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a ) )
& ? [V1e: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Eabs @ V1e ) @ ( c_2Ereal_2E_2F @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ereal_2Epow @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ( ( c_2Emachine__ieee_2Efp64__to__real @ ( c_2Emachine__ieee_2Efp64__sqrt @ c_2Ebinary__ieee_2EroundTiesToEven @ V0a ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Etransc_2Esqrt @ ( c_2Emachine__ieee_2Efp64__to__real @ V0a ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1e ) ) ) ) ) ) ).
%------------------------------------------------------------------------------