ITP001 Axioms: ITP139^5.ax
%------------------------------------------------------------------------------
% File : ITP139^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : float^2.ax [Gau20]
% : HL4139^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 69 ( 13 unt; 3 typ; 0 def)
% Number of atoms : 3295 ( 31 equ; 0 cnn)
% Maximal formula atoms : 120 ( 47 avg)
% Number of connectives : 3579 ( 27 ~; 7 |; 88 &;3398 @)
% ( 11 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 11 avg;3398 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 105 ( 104 usr; 103 con; 0-2 aty)
% Number of variables : 113 ( 6 ^ 98 !; 9 ?; 113 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Efloat_2Eerror,type,
c_2Efloat_2Eerror: $i ).
thf(mem_c_2Efloat_2Eerror,axiom,
mem @ c_2Efloat_2Eerror @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ).
thf(stp_fo_c_2Efloat_2Eerror,type,
fo__c_2Efloat_2Eerror: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
thf(stp_eq_fo_c_2Efloat_2Eerror,axiom,
! [X0: tp__ty_2Erealax_2Ereal] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Efloat_2Eerror @ X0 ) )
= ( ap @ c_2Efloat_2Eerror @ ( inj__ty_2Erealax_2Ereal @ X0 ) ) ) ).
thf(tp_c_2Efloat_2Enormalizes,type,
c_2Efloat_2Enormalizes: $i ).
thf(mem_c_2Efloat_2Enormalizes,axiom,
mem @ c_2Efloat_2Enormalizes @ ( arr @ ty_2Erealax_2Ereal @ bool ) ).
thf(conj_thm_2Efloat_2ESIGN,axiom,
! [V0a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0a ) ) ) ) ).
thf(conj_thm_2Efloat_2EEXPONENT,axiom,
! [V0a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eexponent @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0a ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFRACTION,axiom,
! [V0a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Efraction @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0a ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__VALID,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Eieee_2Eexponent @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Eieee_2Eexpwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Eieee_2Efraction @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Eieee_2Efracwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EVALOF,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ c_2Eieee_2Eexponent @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Eieee_2Ebias @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Eieee_2Efraction @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Eieee_2Efracwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Eieee_2Eexponent @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Eieee_2Ebias @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Eieee_2Efraction @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Eieee_2Efracwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__VALID__DEFLOAT,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] : ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__FINITE__EXPLICIT,axiom,
! [V0a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ c_2Eieee_2Efloat__format ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0a ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Eieee_2Eexponent @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Eieee_2Efraction @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__CASES,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
| ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
| ( p @ ( ap @ c_2Eieee_2EIsnormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
| ( p @ ( ap @ c_2Eieee_2EIsdenormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
| ( p @ ( ap @ c_2Eieee_2EIszero @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__CASES__FINITE,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
| ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
| ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__DISTINCT,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ~ ( ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EIsnormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EIsdenormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EIszero @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EIsnormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EIsdenormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EIszero @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EIsnormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EIsdenormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EIsnormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EIszero @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EIsdenormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EIszero @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__DISTINCT__FINITE,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ~ ( ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
& ~ ( ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__INFINITIES__SIGNED,axiom,
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Esign @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EPlus__infinity ) ) ) )
= fo__c_2Enum_2E0 )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Esign @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EMinus__infinity ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EINFINITY__IS__INFINITY,axiom,
( ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EPlus__infinity ) ) )
& ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EMinus__infinity ) ) ) ) ).
thf(conj_thm_2Efloat_2EZERO__IS__ZERO,axiom,
( ( p @ ( ap @ c_2Eieee_2EIszero @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EPlus__zero ) ) )
& ( p @ ( ap @ c_2Eieee_2EIszero @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EMinus__zero ) ) ) ) ).
thf(conj_thm_2Efloat_2EINFINITY__NOT__NAN,axiom,
( ~ ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EPlus__infinity ) ) )
& ~ ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EMinus__infinity ) ) ) ) ).
thf(conj_thm_2Efloat_2EZERO__NOT__NAN,axiom,
( ~ ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EPlus__zero ) ) )
& ~ ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EMinus__zero ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__INFINITIES,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__eq @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EPlus__infinity ) ) )
| ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__eq @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EMinus__infinity ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__INFINITES__DISTINCT,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
~ ( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__eq @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EPlus__infinity ) ) )
& ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__eq @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EMinus__infinity ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__LT,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__lt @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__GT,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__gt @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__gt @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__LE,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__le @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__GE,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__ge @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__EQ,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__eq @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
<=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__EQ__REFL,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__eq @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
<=> ~ ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__VALID__SPECIAL,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ c_2Eieee_2Eminus__infinity @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ c_2Eieee_2Eplus__infinity @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ c_2Eieee_2Etopfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ c_2Eieee_2Ebottomfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ c_2Eieee_2Eplus__zero @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ c_2Eieee_2Eminus__zero @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__CLOSEST__EXISTS,axiom,
! [V0v: $i] :
( ( mem @ V0v @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Erealax_2Ereal ) )
=> ! [V1x: tp__ty_2Erealax_2Ereal,V2s: $i] :
( ( mem @ V2s @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) )
=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V2s ) )
=> ( ( V2s
!= ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) )
=> ? [V3a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eis__closest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V0v ) @ V2s ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3a ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2ECLOSEST__IS__EVERYTHING,axiom,
! [V0v: $i] :
( ( mem @ V0v @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Erealax_2Ereal ) )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) )
=> ! [V2s: $i] :
( ( mem @ V2s @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) )
=> ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V2s ) )
=> ( ( V2s
!= ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eis__closest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V0v ) @ V2s ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V0v ) @ V1p ) @ V2s ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) ) )
& ( ? [V4b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eis__closest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V0v ) @ V2s ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V4b ) ) )
& ( p @ ( ap @ V1p @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V4b ) ) ) )
=> ( p @ ( ap @ V1p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V0v ) @ V1p ) @ V2s ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2ECLOSEST__IN__SET,axiom,
! [V0v: $i] :
( ( mem @ V0v @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Erealax_2Ereal ) )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) )
=> ! [V2x: tp__ty_2Erealax_2Ereal,V3s: $i] :
( ( mem @ V3s @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) )
=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V3s ) )
=> ( ( V3s
!= ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V0v ) @ V1p ) @ V3s ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) @ V3s ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2ECLOSEST__IS__CLOSEST,axiom,
! [V0v: $i] :
( ( mem @ V0v @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Erealax_2Ereal ) )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) )
=> ! [V2x: tp__ty_2Erealax_2Ereal,V3s: $i] :
( ( mem @ V3s @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) )
=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V3s ) )
=> ( ( V3s
!= ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eis__closest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V0v ) @ V3s ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V0v ) @ V1p ) @ V3s ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__VALID__FINITE,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( p
@ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
@ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V1a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V1a ) @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ V1a ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__FINITE__FINITE,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( p
@ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
@ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V1a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V1a ) @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ V1a ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__VALID__NONEMPTY,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V1a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V1a ) @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ V1a ) ) ) )
!= ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__FINITE__NONEMPTY,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V1a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V1a ) @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ V1a ) ) ) )
!= ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__FINITE__CLOSEST,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1v: $i] :
( ( mem @ V1v @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Erealax_2Ereal ) )
=> ! [V2p: $i] :
( ( mem @ V2p @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) )
=> ! [V3x: tp__ty_2Erealax_2Ereal] :
( p
@ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) )
@ ( ap
@ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V1v ) @ V2p )
@ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V4a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V4a ) @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ V4a ) ) ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V3x ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__VALID__CLOSEST,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1v: $i] :
( ( mem @ V1v @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Erealax_2Ereal ) )
=> ! [V2p: $i] :
( ( mem @ V2p @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) )
=> ! [V3x: tp__ty_2Erealax_2Ereal] :
( p
@ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) )
@ ( ap
@ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ V1v ) @ V2p )
@ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V4a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V4a ) @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ V4a ) ) ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V3x ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EIS__VALID__ROUND,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) ) ).
thf(conj_thm_2Efloat_2EDEFLOAT__FLOAT__ROUND,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Edefloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ).
thf(conj_thm_2Efloat_2EDEFLOAT__FLOAT__ZEROSIGN__ROUND,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Edefloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EVALOF__DEFLOAT__FLOAT__ZEROSIGN__ROUND,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1b: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Eieee_2Evalof @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Eieee_2Evalof @ c_2Eieee_2Efloat__format ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EISFINITE,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EVAL__FINITE,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) @ ( ap @ c_2Eieee_2Elargest @ c_2Eieee_2Efloat__format ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__THRESHOLD__EXPLICIT,axiom,
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__LARGEST__EXPLICIT,axiom,
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2Elargest @ c_2Eieee_2Efloat__format ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EVAL__THRESHOLD,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
=> ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) ) ) ).
thf(ax_thm_2Efloat_2Eerror__def,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Efloat_2Eerror @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Eieee_2EVal @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ).
thf(conj_thm_2Efloat_2EERROR__IS__ZERO,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1x: tp__ty_2Erealax_2Ereal] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= V1x ) )
=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Efloat_2Eerror @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EERROR__BOUND__NORM__STRONG,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1j: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) )
& ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1j ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ c_2Efloat_2Eerror @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1j ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efloat_2Enormalizes__def,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ c_2Efloat_2Enormalizes @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Erealax_2Einv @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Eieee_2Ebias @ c_2Eieee_2Efloat__format ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EREAL__IN__BINADE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ c_2Efloat_2Enormalizes @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
=> ? [V1j: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1j ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Eieee_2Eemax @ c_2Eieee_2Efloat__format ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1j ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1j ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EERROR__BOUND__NORM__STRONG__NORMALIZE,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ c_2Efloat_2Enormalizes @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
=> ? [V1j: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ c_2Efloat_2Eerror @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1j ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2ERELATIVE__ERROR,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ c_2Efloat_2Enormalizes @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
=> ? [V1e: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V1e ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
& ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V1e ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EDEFLOAT__FLOAT__ZEROSIGN__ROUND__FINITE,axiom,
! [V0b: tp__ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__ADD,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
& ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) ) )
=> ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__add @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
& ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( ap @ ( ap @ c_2Eieee_2Efloat__add @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) @ ( ap @ c_2Efloat_2Eerror @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__SUB,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
& ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) ) )
=> ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__sub @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
& ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( ap @ ( ap @ c_2Eieee_2Efloat__sub @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) @ ( ap @ c_2Efloat_2Eerror @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__MUL,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
& ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) ) )
=> ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__mul @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
& ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( ap @ ( ap @ c_2Eieee_2Efloat__mul @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) @ ( ap @ c_2Efloat_2Eerror @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__DIV,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
& ~ ( p @ ( ap @ c_2Eieee_2EIszero @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
& ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) ) )
=> ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__div @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
& ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( ap @ ( ap @ c_2Eieee_2Efloat__div @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) @ ( ap @ c_2Efloat_2Eerror @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__ADD__FINITE,axiom,
! [V0b: tp__ty_2Eieee_2Efloat,V1a: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0b ) ) )
& ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0b ) ) ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) ) )
=> ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__add @ ( inj__ty_2Eieee_2Efloat @ V1a ) ) @ ( inj__ty_2Eieee_2Efloat @ V0b ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__SUB__FINITE,axiom,
! [V0b: tp__ty_2Eieee_2Efloat,V1a: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0b ) ) )
& ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0b ) ) ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) ) )
=> ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__sub @ ( inj__ty_2Eieee_2Efloat @ V1a ) ) @ ( inj__ty_2Eieee_2Efloat @ V0b ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__MUL__FINITE,axiom,
! [V0b: tp__ty_2Eieee_2Efloat,V1a: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0b ) ) )
& ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0b ) ) ) ) ) @ ( ap @ c_2Eieee_2Ethreshold @ c_2Eieee_2Efloat__format ) ) ) )
=> ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__mul @ ( inj__ty_2Eieee_2Efloat @ V1a ) ) @ ( inj__ty_2Eieee_2Efloat @ V0b ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__ADD__RELATIVE,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
& ( p @ ( ap @ c_2Efloat_2Enormalizes @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) )
=> ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__add @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
& ? [V2e: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
& ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( ap @ ( ap @ c_2Eieee_2Efloat__add @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__SUB__RELATIVE,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
& ( p @ ( ap @ c_2Efloat_2Enormalizes @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) )
=> ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__sub @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
& ? [V2e: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
& ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( ap @ ( ap @ c_2Eieee_2Efloat__sub @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__MUL__RELATIVE,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
& ( p @ ( ap @ c_2Efloat_2Enormalizes @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) )
=> ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__mul @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
& ? [V2e: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
& ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( ap @ ( ap @ c_2Eieee_2Efloat__mul @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efloat_2EFLOAT__DIV__RELATIVE,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
& ( p @ ( ap @ c_2Eieee_2EFinite @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
& ~ ( p @ ( ap @ c_2Eieee_2EIszero @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
& ( p @ ( ap @ c_2Efloat_2Enormalizes @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) )
=> ( ( p @ ( ap @ c_2Eieee_2EFinite @ ( ap @ ( ap @ c_2Eieee_2Efloat__div @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
& ? [V2e: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Epow @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
& ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( ap @ ( ap @ c_2Eieee_2Efloat__div @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2e ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------