ITP001 Axioms: ITP136^5.ax
%------------------------------------------------------------------------------
% File : ITP136^5 : 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 : ieee^2.ax [Gau20]
% : HL4136^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 454 ( 123 unt; 164 typ; 0 def)
% Number of atoms : 5430 ( 256 equ; 0 cnn)
% Maximal formula atoms : 62 ( 11 avg)
% Number of connectives : 7223 ( 14 ~; 18 |; 86 &;6955 @)
% ( 45 <=>; 105 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg;6955 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 227 ( 226 usr; 179 con; 0-3 aty)
% Number of variables : 405 ( 31 ^ 364 !; 10 ?; 405 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_ty_2Eieee_2Eccode,type,
ty_2Eieee_2Eccode: del ).
thf(tp_ty_2Eieee_2Efloat,type,
ty_2Eieee_2Efloat: del ).
thf(tp_ty_2Eieee_2Eroundmode,type,
ty_2Eieee_2Eroundmode: del ).
thf(stp_ty_2Eieee_2Eccode,type,
tp__ty_2Eieee_2Eccode: $tType ).
thf(stp_inj_ty_2Eieee_2Eccode,type,
inj__ty_2Eieee_2Eccode: tp__ty_2Eieee_2Eccode > $i ).
thf(stp_surj_ty_2Eieee_2Eccode,type,
surj__ty_2Eieee_2Eccode: $i > tp__ty_2Eieee_2Eccode ).
thf(stp_inj_surj_ty_2Eieee_2Eccode,axiom,
! [X: tp__ty_2Eieee_2Eccode] :
( ( surj__ty_2Eieee_2Eccode @ ( inj__ty_2Eieee_2Eccode @ X ) )
= X ) ).
thf(stp_inj_mem_ty_2Eieee_2Eccode,axiom,
! [X: tp__ty_2Eieee_2Eccode] : ( mem @ ( inj__ty_2Eieee_2Eccode @ X ) @ ty_2Eieee_2Eccode ) ).
thf(stp_iso_mem_ty_2Eieee_2Eccode,axiom,
! [X: $i] :
( ( mem @ X @ ty_2Eieee_2Eccode )
=> ( X
= ( inj__ty_2Eieee_2Eccode @ ( surj__ty_2Eieee_2Eccode @ X ) ) ) ) ).
thf(tp_c_2Eieee_2EEq,type,
c_2Eieee_2EEq: $i ).
thf(mem_c_2Eieee_2EEq,axiom,
mem @ c_2Eieee_2EEq @ ty_2Eieee_2Eccode ).
thf(stp_fo_c_2Eieee_2EEq,type,
fo__c_2Eieee_2EEq: tp__ty_2Eieee_2Eccode ).
thf(stp_eq_fo_c_2Eieee_2EEq,axiom,
( ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EEq )
= c_2Eieee_2EEq ) ).
thf(stp_ty_2Eieee_2Efloat,type,
tp__ty_2Eieee_2Efloat: $tType ).
thf(stp_inj_ty_2Eieee_2Efloat,type,
inj__ty_2Eieee_2Efloat: tp__ty_2Eieee_2Efloat > $i ).
thf(stp_surj_ty_2Eieee_2Efloat,type,
surj__ty_2Eieee_2Efloat: $i > tp__ty_2Eieee_2Efloat ).
thf(stp_inj_surj_ty_2Eieee_2Efloat,axiom,
! [X: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( inj__ty_2Eieee_2Efloat @ X ) )
= X ) ).
thf(stp_inj_mem_ty_2Eieee_2Efloat,axiom,
! [X: tp__ty_2Eieee_2Efloat] : ( mem @ ( inj__ty_2Eieee_2Efloat @ X ) @ ty_2Eieee_2Efloat ) ).
thf(stp_iso_mem_ty_2Eieee_2Efloat,axiom,
! [X: $i] :
( ( mem @ X @ ty_2Eieee_2Efloat )
=> ( X
= ( inj__ty_2Eieee_2Efloat @ ( surj__ty_2Eieee_2Efloat @ X ) ) ) ) ).
thf(tp_c_2Eieee_2EExponent,type,
c_2Eieee_2EExponent: $i ).
thf(mem_c_2Eieee_2EExponent,axiom,
mem @ c_2Eieee_2EExponent @ ( arr @ ty_2Eieee_2Efloat @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2EExponent,type,
fo__c_2Eieee_2EExponent: tp__ty_2Eieee_2Efloat > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2EExponent,axiom,
! [X0: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2EExponent @ X0 ) )
= ( ap @ c_2Eieee_2EExponent @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) ) ).
thf(tp_c_2Eieee_2EFinite,type,
c_2Eieee_2EFinite: $i ).
thf(mem_c_2Eieee_2EFinite,axiom,
mem @ c_2Eieee_2EFinite @ ( arr @ ty_2Eieee_2Efloat @ bool ) ).
thf(tp_c_2Eieee_2EFloat,type,
c_2Eieee_2EFloat: $i ).
thf(mem_c_2Eieee_2EFloat,axiom,
mem @ c_2Eieee_2EFloat @ ( arr @ ty_2Erealax_2Ereal @ ty_2Eieee_2Efloat ) ).
thf(stp_fo_c_2Eieee_2EFloat,type,
fo__c_2Eieee_2EFloat: tp__ty_2Erealax_2Ereal > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2EFloat,axiom,
! [X0: tp__ty_2Erealax_2Ereal] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2EFloat @ X0 ) )
= ( ap @ c_2Eieee_2EFloat @ ( inj__ty_2Erealax_2Ereal @ X0 ) ) ) ).
thf(tp_c_2Eieee_2EFraction,type,
c_2Eieee_2EFraction: $i ).
thf(mem_c_2Eieee_2EFraction,axiom,
mem @ c_2Eieee_2EFraction @ ( arr @ ty_2Eieee_2Efloat @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2EFraction,type,
fo__c_2Eieee_2EFraction: tp__ty_2Eieee_2Efloat > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2EFraction,axiom,
! [X0: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2EFraction @ X0 ) )
= ( ap @ c_2Eieee_2EFraction @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) ) ).
thf(tp_c_2Eieee_2EGt,type,
c_2Eieee_2EGt: $i ).
thf(mem_c_2Eieee_2EGt,axiom,
mem @ c_2Eieee_2EGt @ ty_2Eieee_2Eccode ).
thf(stp_fo_c_2Eieee_2EGt,type,
fo__c_2Eieee_2EGt: tp__ty_2Eieee_2Eccode ).
thf(stp_eq_fo_c_2Eieee_2EGt,axiom,
( ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EGt )
= c_2Eieee_2EGt ) ).
thf(tp_c_2Eieee_2EInfinity,type,
c_2Eieee_2EInfinity: $i ).
thf(mem_c_2Eieee_2EInfinity,axiom,
mem @ c_2Eieee_2EInfinity @ ( arr @ ty_2Eieee_2Efloat @ bool ) ).
thf(tp_c_2Eieee_2EIsdenormal,type,
c_2Eieee_2EIsdenormal: $i ).
thf(mem_c_2Eieee_2EIsdenormal,axiom,
mem @ c_2Eieee_2EIsdenormal @ ( arr @ ty_2Eieee_2Efloat @ bool ) ).
thf(tp_c_2Eieee_2EIsintegral,type,
c_2Eieee_2EIsintegral: $i ).
thf(mem_c_2Eieee_2EIsintegral,axiom,
mem @ c_2Eieee_2EIsintegral @ ( arr @ ty_2Eieee_2Efloat @ bool ) ).
thf(tp_c_2Eieee_2EIsnan,type,
c_2Eieee_2EIsnan: $i ).
thf(mem_c_2Eieee_2EIsnan,axiom,
mem @ c_2Eieee_2EIsnan @ ( arr @ ty_2Eieee_2Efloat @ bool ) ).
thf(tp_c_2Eieee_2EIsnormal,type,
c_2Eieee_2EIsnormal: $i ).
thf(mem_c_2Eieee_2EIsnormal,axiom,
mem @ c_2Eieee_2EIsnormal @ ( arr @ ty_2Eieee_2Efloat @ bool ) ).
thf(tp_c_2Eieee_2EIszero,type,
c_2Eieee_2EIszero: $i ).
thf(mem_c_2Eieee_2EIszero,axiom,
mem @ c_2Eieee_2EIszero @ ( arr @ ty_2Eieee_2Efloat @ bool ) ).
thf(tp_c_2Eieee_2ELt,type,
c_2Eieee_2ELt: $i ).
thf(mem_c_2Eieee_2ELt,axiom,
mem @ c_2Eieee_2ELt @ ty_2Eieee_2Eccode ).
thf(stp_fo_c_2Eieee_2ELt,type,
fo__c_2Eieee_2ELt: tp__ty_2Eieee_2Eccode ).
thf(stp_eq_fo_c_2Eieee_2ELt,axiom,
( ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2ELt )
= c_2Eieee_2ELt ) ).
thf(tp_c_2Eieee_2EMinus__infinity,type,
c_2Eieee_2EMinus__infinity: $i ).
thf(mem_c_2Eieee_2EMinus__infinity,axiom,
mem @ c_2Eieee_2EMinus__infinity @ ty_2Eieee_2Efloat ).
thf(stp_fo_c_2Eieee_2EMinus__infinity,type,
fo__c_2Eieee_2EMinus__infinity: tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2EMinus__infinity,axiom,
( ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EMinus__infinity )
= c_2Eieee_2EMinus__infinity ) ).
thf(tp_c_2Eieee_2EMinus__zero,type,
c_2Eieee_2EMinus__zero: $i ).
thf(mem_c_2Eieee_2EMinus__zero,axiom,
mem @ c_2Eieee_2EMinus__zero @ ty_2Eieee_2Efloat ).
thf(stp_fo_c_2Eieee_2EMinus__zero,type,
fo__c_2Eieee_2EMinus__zero: tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2EMinus__zero,axiom,
( ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EMinus__zero )
= c_2Eieee_2EMinus__zero ) ).
thf(tp_c_2Eieee_2EPlus__infinity,type,
c_2Eieee_2EPlus__infinity: $i ).
thf(mem_c_2Eieee_2EPlus__infinity,axiom,
mem @ c_2Eieee_2EPlus__infinity @ ty_2Eieee_2Efloat ).
thf(stp_fo_c_2Eieee_2EPlus__infinity,type,
fo__c_2Eieee_2EPlus__infinity: tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2EPlus__infinity,axiom,
( ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EPlus__infinity )
= c_2Eieee_2EPlus__infinity ) ).
thf(tp_c_2Eieee_2EPlus__zero,type,
c_2Eieee_2EPlus__zero: $i ).
thf(mem_c_2Eieee_2EPlus__zero,axiom,
mem @ c_2Eieee_2EPlus__zero @ ty_2Eieee_2Efloat ).
thf(stp_fo_c_2Eieee_2EPlus__zero,type,
fo__c_2Eieee_2EPlus__zero: tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2EPlus__zero,axiom,
( ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EPlus__zero )
= c_2Eieee_2EPlus__zero ) ).
thf(tp_c_2Eieee_2EROUNDFLOAT,type,
c_2Eieee_2EROUNDFLOAT: $i ).
thf(mem_c_2Eieee_2EROUNDFLOAT,axiom,
mem @ c_2Eieee_2EROUNDFLOAT @ ( arr @ ty_2Eieee_2Efloat @ ty_2Eieee_2Efloat ) ).
thf(stp_fo_c_2Eieee_2EROUNDFLOAT,type,
fo__c_2Eieee_2EROUNDFLOAT: tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2EROUNDFLOAT,axiom,
! [X0: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2EROUNDFLOAT @ X0 ) )
= ( ap @ c_2Eieee_2EROUNDFLOAT @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) ) ).
thf(tp_c_2Eieee_2ESign,type,
c_2Eieee_2ESign: $i ).
thf(mem_c_2Eieee_2ESign,axiom,
mem @ c_2Eieee_2ESign @ ( arr @ ty_2Eieee_2Efloat @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2ESign,type,
fo__c_2Eieee_2ESign: tp__ty_2Eieee_2Efloat > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2ESign,axiom,
! [X0: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2ESign @ X0 ) )
= ( ap @ c_2Eieee_2ESign @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) ) ).
thf(stp_ty_2Eieee_2Eroundmode,type,
tp__ty_2Eieee_2Eroundmode: $tType ).
thf(stp_inj_ty_2Eieee_2Eroundmode,type,
inj__ty_2Eieee_2Eroundmode: tp__ty_2Eieee_2Eroundmode > $i ).
thf(stp_surj_ty_2Eieee_2Eroundmode,type,
surj__ty_2Eieee_2Eroundmode: $i > tp__ty_2Eieee_2Eroundmode ).
thf(stp_inj_surj_ty_2Eieee_2Eroundmode,axiom,
! [X: tp__ty_2Eieee_2Eroundmode] :
( ( surj__ty_2Eieee_2Eroundmode @ ( inj__ty_2Eieee_2Eroundmode @ X ) )
= X ) ).
thf(stp_inj_mem_ty_2Eieee_2Eroundmode,axiom,
! [X: tp__ty_2Eieee_2Eroundmode] : ( mem @ ( inj__ty_2Eieee_2Eroundmode @ X ) @ ty_2Eieee_2Eroundmode ) ).
thf(stp_iso_mem_ty_2Eieee_2Eroundmode,axiom,
! [X: $i] :
( ( mem @ X @ ty_2Eieee_2Eroundmode )
=> ( X
= ( inj__ty_2Eieee_2Eroundmode @ ( surj__ty_2Eieee_2Eroundmode @ X ) ) ) ) ).
thf(tp_c_2Eieee_2ETo__nearest,type,
c_2Eieee_2ETo__nearest: $i ).
thf(mem_c_2Eieee_2ETo__nearest,axiom,
mem @ c_2Eieee_2ETo__nearest @ ty_2Eieee_2Eroundmode ).
thf(stp_fo_c_2Eieee_2ETo__nearest,type,
fo__c_2Eieee_2ETo__nearest: tp__ty_2Eieee_2Eroundmode ).
thf(stp_eq_fo_c_2Eieee_2ETo__nearest,axiom,
( ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest )
= c_2Eieee_2ETo__nearest ) ).
thf(tp_c_2Eieee_2ETo__ninfinity,type,
c_2Eieee_2ETo__ninfinity: $i ).
thf(mem_c_2Eieee_2ETo__ninfinity,axiom,
mem @ c_2Eieee_2ETo__ninfinity @ ty_2Eieee_2Eroundmode ).
thf(stp_fo_c_2Eieee_2ETo__ninfinity,type,
fo__c_2Eieee_2ETo__ninfinity: tp__ty_2Eieee_2Eroundmode ).
thf(stp_eq_fo_c_2Eieee_2ETo__ninfinity,axiom,
( ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__ninfinity )
= c_2Eieee_2ETo__ninfinity ) ).
thf(tp_c_2Eieee_2ETo__pinfinity,type,
c_2Eieee_2ETo__pinfinity: $i ).
thf(mem_c_2Eieee_2ETo__pinfinity,axiom,
mem @ c_2Eieee_2ETo__pinfinity @ ty_2Eieee_2Eroundmode ).
thf(stp_fo_c_2Eieee_2ETo__pinfinity,type,
fo__c_2Eieee_2ETo__pinfinity: tp__ty_2Eieee_2Eroundmode ).
thf(stp_eq_fo_c_2Eieee_2ETo__pinfinity,axiom,
( ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__pinfinity )
= c_2Eieee_2ETo__pinfinity ) ).
thf(tp_c_2Eieee_2EUlp,type,
c_2Eieee_2EUlp: $i ).
thf(mem_c_2Eieee_2EUlp,axiom,
mem @ c_2Eieee_2EUlp @ ( arr @ ty_2Eieee_2Efloat @ ty_2Erealax_2Ereal ) ).
thf(stp_fo_c_2Eieee_2EUlp,type,
fo__c_2Eieee_2EUlp: tp__ty_2Eieee_2Efloat > tp__ty_2Erealax_2Ereal ).
thf(stp_eq_fo_c_2Eieee_2EUlp,axiom,
! [X0: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Eieee_2EUlp @ X0 ) )
= ( ap @ c_2Eieee_2EUlp @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) ) ).
thf(tp_c_2Eieee_2EUn,type,
c_2Eieee_2EUn: $i ).
thf(mem_c_2Eieee_2EUn,axiom,
mem @ c_2Eieee_2EUn @ ty_2Eieee_2Eccode ).
thf(stp_fo_c_2Eieee_2EUn,type,
fo__c_2Eieee_2EUn: tp__ty_2Eieee_2Eccode ).
thf(stp_eq_fo_c_2Eieee_2EUn,axiom,
( ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EUn )
= c_2Eieee_2EUn ) ).
thf(tp_c_2Eieee_2EVal,type,
c_2Eieee_2EVal: $i ).
thf(mem_c_2Eieee_2EVal,axiom,
mem @ c_2Eieee_2EVal @ ( arr @ ty_2Eieee_2Efloat @ ty_2Erealax_2Ereal ) ).
thf(stp_fo_c_2Eieee_2EVal,type,
fo__c_2Eieee_2EVal: tp__ty_2Eieee_2Efloat > tp__ty_2Erealax_2Ereal ).
thf(stp_eq_fo_c_2Eieee_2EVal,axiom,
! [X0: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Eieee_2EVal @ X0 ) )
= ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Ebias,type,
c_2Eieee_2Ebias: $i ).
thf(mem_c_2Eieee_2Ebias,axiom,
mem @ c_2Eieee_2Ebias @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Ebias,type,
fo__c_2Eieee_2Ebias: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Ebias,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Ebias @ X0 ) )
= ( ap @ c_2Eieee_2Ebias @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Ebottomfloat,type,
c_2Eieee_2Ebottomfloat: $i ).
thf(mem_c_2Eieee_2Ebottomfloat,axiom,
mem @ c_2Eieee_2Ebottomfloat @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Eieee_2Eccode2num,type,
c_2Eieee_2Eccode2num: $i ).
thf(mem_c_2Eieee_2Eccode2num,axiom,
mem @ c_2Eieee_2Eccode2num @ ( arr @ ty_2Eieee_2Eccode @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Eccode2num,type,
fo__c_2Eieee_2Eccode2num: tp__ty_2Eieee_2Eccode > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Eccode2num,axiom,
! [X0: tp__ty_2Eieee_2Eccode] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Eccode2num @ X0 ) )
= ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Eccode__CASE,type,
c_2Eieee_2Eccode__CASE: del > $i ).
thf(mem_c_2Eieee_2Eccode__CASE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eieee_2Eccode__CASE @ A_27a ) @ ( arr @ ty_2Eieee_2Eccode @ ( arr @ A_27a @ ( arr @ A_27a @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) ) ) ).
thf(tp_c_2Eieee_2Eccode__size,type,
c_2Eieee_2Eccode__size: $i ).
thf(mem_c_2Eieee_2Eccode__size,axiom,
mem @ c_2Eieee_2Eccode__size @ ( arr @ ty_2Eieee_2Eccode @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Eccode__size,type,
fo__c_2Eieee_2Eccode__size: tp__ty_2Eieee_2Eccode > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Eccode__size,axiom,
! [X0: tp__ty_2Eieee_2Eccode] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Eccode__size @ X0 ) )
= ( ap @ c_2Eieee_2Eccode__size @ ( inj__ty_2Eieee_2Eccode @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Eclosest,type,
c_2Eieee_2Eclosest: del > $i ).
thf(mem_c_2Eieee_2Eclosest,axiom,
! [A_27a: del] : ( mem @ ( c_2Eieee_2Eclosest @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ty_2Erealax_2Ereal @ A_27a ) ) ) ) ) ).
thf(tp_c_2Eieee_2Edefloat,type,
c_2Eieee_2Edefloat: $i ).
thf(mem_c_2Eieee_2Edefloat,axiom,
mem @ c_2Eieee_2Edefloat @ ( arr @ ty_2Eieee_2Efloat @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Eieee_2Eemax,type,
c_2Eieee_2Eemax: $i ).
thf(mem_c_2Eieee_2Eemax,axiom,
mem @ c_2Eieee_2Eemax @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Eemax,type,
fo__c_2Eieee_2Eemax: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Eemax,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Eemax @ X0 ) )
= ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Eencoding,type,
c_2Eieee_2Eencoding: $i ).
thf(mem_c_2Eieee_2Eencoding,axiom,
mem @ c_2Eieee_2Eencoding @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Enum_2Enum ) ) ).
thf(stp_fo_c_2Eieee_2Eencoding,type,
fo__c_2Eieee_2Eencoding: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Eencoding,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,X1: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Eencoding @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Eieee_2Eencoding @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X1 ) ) ) ).
thf(tp_c_2Eieee_2Eexponent,type,
c_2Eieee_2Eexponent: $i ).
thf(mem_c_2Eieee_2Eexponent,axiom,
mem @ c_2Eieee_2Eexponent @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Eexponent,type,
fo__c_2Eieee_2Eexponent: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Eexponent,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Eexponent @ X0 ) )
= ( ap @ c_2Eieee_2Eexponent @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Eexpwidth,type,
c_2Eieee_2Eexpwidth: $i ).
thf(mem_c_2Eieee_2Eexpwidth,axiom,
mem @ c_2Eieee_2Eexpwidth @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Eexpwidth,type,
fo__c_2Eieee_2Eexpwidth: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Eexpwidth,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Eexpwidth @ X0 ) )
= ( ap @ c_2Eieee_2Eexpwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Efadd,type,
c_2Eieee_2Efadd: $i ).
thf(mem_c_2Eieee_2Efadd,axiom,
mem @ c_2Eieee_2Efadd @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Eieee_2Efcompare,type,
c_2Eieee_2Efcompare: $i ).
thf(mem_c_2Eieee_2Efcompare,axiom,
mem @ c_2Eieee_2Efcompare @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Eieee_2Eccode ) ) ) ).
thf(stp_fo_c_2Eieee_2Efcompare,type,
fo__c_2Eieee_2Efcompare: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Eieee_2Eccode ).
thf(stp_eq_fo_c_2Eieee_2Efcompare,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,X1: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,X2: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Eieee_2Eccode @ ( fo__c_2Eieee_2Efcompare @ X0 @ X1 @ X2 ) )
= ( ap @ ( ap @ ( ap @ c_2Eieee_2Efcompare @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X1 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X2 ) ) ) ).
thf(tp_c_2Eieee_2Efdiv,type,
c_2Eieee_2Efdiv: $i ).
thf(mem_c_2Eieee_2Efdiv,axiom,
mem @ c_2Eieee_2Efdiv @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Eieee_2Efeq,type,
c_2Eieee_2Efeq: $i ).
thf(mem_c_2Eieee_2Efeq,axiom,
mem @ c_2Eieee_2Efeq @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ) ).
thf(tp_c_2Eieee_2Efge,type,
c_2Eieee_2Efge: $i ).
thf(mem_c_2Eieee_2Efge,axiom,
mem @ c_2Eieee_2Efge @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ) ).
thf(tp_c_2Eieee_2Efgt,type,
c_2Eieee_2Efgt: $i ).
thf(mem_c_2Eieee_2Efgt,axiom,
mem @ c_2Eieee_2Efgt @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ) ).
thf(tp_c_2Eieee_2Efintrnd,type,
c_2Eieee_2Efintrnd: $i ).
thf(mem_c_2Eieee_2Efintrnd,axiom,
mem @ c_2Eieee_2Efintrnd @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ( 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 ) ) ) ) ) ).
thf(tp_c_2Eieee_2Efle,type,
c_2Eieee_2Efle: $i ).
thf(mem_c_2Eieee_2Efle,axiom,
mem @ c_2Eieee_2Efle @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ) ).
thf(tp_c_2Eieee_2Efloat,type,
c_2Eieee_2Efloat: $i ).
thf(mem_c_2Eieee_2Efloat,axiom,
mem @ c_2Eieee_2Efloat @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Eieee_2Efloat ) ).
thf(stp_fo_c_2Eieee_2Efloat,type,
fo__c_2Eieee_2Efloat: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2Efloat,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2Efloat @ X0 ) )
= ( ap @ c_2Eieee_2Efloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Efloat__To__zero,type,
c_2Eieee_2Efloat__To__zero: $i ).
thf(mem_c_2Eieee_2Efloat__To__zero,axiom,
mem @ c_2Eieee_2Efloat__To__zero @ ty_2Eieee_2Eroundmode ).
thf(stp_fo_c_2Eieee_2Efloat__To__zero,type,
fo__c_2Eieee_2Efloat__To__zero: tp__ty_2Eieee_2Eroundmode ).
thf(stp_eq_fo_c_2Eieee_2Efloat__To__zero,axiom,
( ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2Efloat__To__zero )
= c_2Eieee_2Efloat__To__zero ) ).
thf(tp_c_2Eieee_2Efloat__abs,type,
c_2Eieee_2Efloat__abs: $i ).
thf(mem_c_2Eieee_2Efloat__abs,axiom,
mem @ c_2Eieee_2Efloat__abs @ ( arr @ ty_2Eieee_2Efloat @ ty_2Eieee_2Efloat ) ).
thf(stp_fo_c_2Eieee_2Efloat__abs,type,
fo__c_2Eieee_2Efloat__abs: tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2Efloat__abs,axiom,
! [X0: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2Efloat__abs @ X0 ) )
= ( ap @ c_2Eieee_2Efloat__abs @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Efloat__add,type,
c_2Eieee_2Efloat__add: $i ).
thf(mem_c_2Eieee_2Efloat__add,axiom,
mem @ c_2Eieee_2Efloat__add @ ( arr @ ty_2Eieee_2Efloat @ ( arr @ ty_2Eieee_2Efloat @ ty_2Eieee_2Efloat ) ) ).
thf(stp_fo_c_2Eieee_2Efloat__add,type,
fo__c_2Eieee_2Efloat__add: tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2Efloat__add,axiom,
! [X0: tp__ty_2Eieee_2Efloat,X1: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2Efloat__add @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Eieee_2Efloat__add @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) @ ( inj__ty_2Eieee_2Efloat @ X1 ) ) ) ).
thf(tp_c_2Eieee_2Efloat__div,type,
c_2Eieee_2Efloat__div: $i ).
thf(mem_c_2Eieee_2Efloat__div,axiom,
mem @ c_2Eieee_2Efloat__div @ ( arr @ ty_2Eieee_2Efloat @ ( arr @ ty_2Eieee_2Efloat @ ty_2Eieee_2Efloat ) ) ).
thf(stp_fo_c_2Eieee_2Efloat__div,type,
fo__c_2Eieee_2Efloat__div: tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2Efloat__div,axiom,
! [X0: tp__ty_2Eieee_2Efloat,X1: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2Efloat__div @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Eieee_2Efloat__div @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) @ ( inj__ty_2Eieee_2Efloat @ X1 ) ) ) ).
thf(tp_c_2Eieee_2Efloat__eq,type,
c_2Eieee_2Efloat__eq: $i ).
thf(mem_c_2Eieee_2Efloat__eq,axiom,
mem @ c_2Eieee_2Efloat__eq @ ( arr @ ty_2Eieee_2Efloat @ ( arr @ ty_2Eieee_2Efloat @ bool ) ) ).
thf(tp_c_2Eieee_2Efloat__format,type,
c_2Eieee_2Efloat__format: $i ).
thf(mem_c_2Eieee_2Efloat__format,axiom,
mem @ c_2Eieee_2Efloat__format @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
thf(tp_c_2Eieee_2Efloat__ge,type,
c_2Eieee_2Efloat__ge: $i ).
thf(mem_c_2Eieee_2Efloat__ge,axiom,
mem @ c_2Eieee_2Efloat__ge @ ( arr @ ty_2Eieee_2Efloat @ ( arr @ ty_2Eieee_2Efloat @ bool ) ) ).
thf(tp_c_2Eieee_2Efloat__gt,type,
c_2Eieee_2Efloat__gt: $i ).
thf(mem_c_2Eieee_2Efloat__gt,axiom,
mem @ c_2Eieee_2Efloat__gt @ ( arr @ ty_2Eieee_2Efloat @ ( arr @ ty_2Eieee_2Efloat @ bool ) ) ).
thf(tp_c_2Eieee_2Efloat__le,type,
c_2Eieee_2Efloat__le: $i ).
thf(mem_c_2Eieee_2Efloat__le,axiom,
mem @ c_2Eieee_2Efloat__le @ ( arr @ ty_2Eieee_2Efloat @ ( arr @ ty_2Eieee_2Efloat @ bool ) ) ).
thf(tp_c_2Eieee_2Efloat__lt,type,
c_2Eieee_2Efloat__lt: $i ).
thf(mem_c_2Eieee_2Efloat__lt,axiom,
mem @ c_2Eieee_2Efloat__lt @ ( arr @ ty_2Eieee_2Efloat @ ( arr @ ty_2Eieee_2Efloat @ bool ) ) ).
thf(tp_c_2Eieee_2Efloat__mul,type,
c_2Eieee_2Efloat__mul: $i ).
thf(mem_c_2Eieee_2Efloat__mul,axiom,
mem @ c_2Eieee_2Efloat__mul @ ( arr @ ty_2Eieee_2Efloat @ ( arr @ ty_2Eieee_2Efloat @ ty_2Eieee_2Efloat ) ) ).
thf(stp_fo_c_2Eieee_2Efloat__mul,type,
fo__c_2Eieee_2Efloat__mul: tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2Efloat__mul,axiom,
! [X0: tp__ty_2Eieee_2Efloat,X1: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2Efloat__mul @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Eieee_2Efloat__mul @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) @ ( inj__ty_2Eieee_2Efloat @ X1 ) ) ) ).
thf(tp_c_2Eieee_2Efloat__neg,type,
c_2Eieee_2Efloat__neg: $i ).
thf(mem_c_2Eieee_2Efloat__neg,axiom,
mem @ c_2Eieee_2Efloat__neg @ ( arr @ ty_2Eieee_2Efloat @ ty_2Eieee_2Efloat ) ).
thf(stp_fo_c_2Eieee_2Efloat__neg,type,
fo__c_2Eieee_2Efloat__neg: tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2Efloat__neg,axiom,
! [X0: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2Efloat__neg @ X0 ) )
= ( ap @ c_2Eieee_2Efloat__neg @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Efloat__rem,type,
c_2Eieee_2Efloat__rem: $i ).
thf(mem_c_2Eieee_2Efloat__rem,axiom,
mem @ c_2Eieee_2Efloat__rem @ ( arr @ ty_2Eieee_2Efloat @ ( arr @ ty_2Eieee_2Efloat @ ty_2Eieee_2Efloat ) ) ).
thf(stp_fo_c_2Eieee_2Efloat__rem,type,
fo__c_2Eieee_2Efloat__rem: tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2Efloat__rem,axiom,
! [X0: tp__ty_2Eieee_2Efloat,X1: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2Efloat__rem @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Eieee_2Efloat__rem @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) @ ( inj__ty_2Eieee_2Efloat @ X1 ) ) ) ).
thf(tp_c_2Eieee_2Efloat__sqrt,type,
c_2Eieee_2Efloat__sqrt: $i ).
thf(mem_c_2Eieee_2Efloat__sqrt,axiom,
mem @ c_2Eieee_2Efloat__sqrt @ ( arr @ ty_2Eieee_2Efloat @ ty_2Eieee_2Efloat ) ).
thf(stp_fo_c_2Eieee_2Efloat__sqrt,type,
fo__c_2Eieee_2Efloat__sqrt: tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2Efloat__sqrt,axiom,
! [X0: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2Efloat__sqrt @ X0 ) )
= ( ap @ c_2Eieee_2Efloat__sqrt @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Efloat__sub,type,
c_2Eieee_2Efloat__sub: $i ).
thf(mem_c_2Eieee_2Efloat__sub,axiom,
mem @ c_2Eieee_2Efloat__sub @ ( arr @ ty_2Eieee_2Efloat @ ( arr @ ty_2Eieee_2Efloat @ ty_2Eieee_2Efloat ) ) ).
thf(stp_fo_c_2Eieee_2Efloat__sub,type,
fo__c_2Eieee_2Efloat__sub: tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat > tp__ty_2Eieee_2Efloat ).
thf(stp_eq_fo_c_2Eieee_2Efloat__sub,axiom,
! [X0: tp__ty_2Eieee_2Efloat,X1: tp__ty_2Eieee_2Efloat] :
( ( inj__ty_2Eieee_2Efloat @ ( fo__c_2Eieee_2Efloat__sub @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Eieee_2Efloat__sub @ ( inj__ty_2Eieee_2Efloat @ X0 ) ) @ ( inj__ty_2Eieee_2Efloat @ X1 ) ) ) ).
thf(tp_c_2Eieee_2Eflt,type,
c_2Eieee_2Eflt: $i ).
thf(mem_c_2Eieee_2Eflt,axiom,
mem @ c_2Eieee_2Eflt @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ) ).
thf(tp_c_2Eieee_2Efmul,type,
c_2Eieee_2Efmul: $i ).
thf(mem_c_2Eieee_2Efmul,axiom,
mem @ c_2Eieee_2Efmul @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Eieee_2Efneg,type,
c_2Eieee_2Efneg: $i ).
thf(mem_c_2Eieee_2Efneg,axiom,
mem @ c_2Eieee_2Efneg @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ( 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 ) ) ) ) ) ).
thf(tp_c_2Eieee_2Efraction,type,
c_2Eieee_2Efraction: $i ).
thf(mem_c_2Eieee_2Efraction,axiom,
mem @ c_2Eieee_2Efraction @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Efraction,type,
fo__c_2Eieee_2Efraction: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Efraction,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Efraction @ X0 ) )
= ( ap @ c_2Eieee_2Efraction @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Efracwidth,type,
c_2Eieee_2Efracwidth: $i ).
thf(mem_c_2Eieee_2Efracwidth,axiom,
mem @ c_2Eieee_2Efracwidth @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Efracwidth,type,
fo__c_2Eieee_2Efracwidth: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Efracwidth,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Efracwidth @ X0 ) )
= ( ap @ c_2Eieee_2Efracwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Efrem,type,
c_2Eieee_2Efrem: $i ).
thf(mem_c_2Eieee_2Efrem,axiom,
mem @ c_2Eieee_2Efrem @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Eieee_2Efsqrt,type,
c_2Eieee_2Efsqrt: $i ).
thf(mem_c_2Eieee_2Efsqrt,axiom,
mem @ c_2Eieee_2Efsqrt @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ( 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 ) ) ) ) ) ).
thf(tp_c_2Eieee_2Efsub,type,
c_2Eieee_2Efsub: $i ).
thf(mem_c_2Eieee_2Efsub,axiom,
mem @ c_2Eieee_2Efsub @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( arr @ ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Eieee_2Eintround,type,
c_2Eieee_2Eintround: $i ).
thf(mem_c_2Eieee_2Eintround,axiom,
mem @ c_2Eieee_2Eintround @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ty_2Erealax_2Ereal @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ) ) ).
thf(tp_c_2Eieee_2Eis__closest,type,
c_2Eieee_2Eis__closest: del > $i ).
thf(mem_c_2Eieee_2Eis__closest,axiom,
! [A_27a: del] : ( mem @ ( c_2Eieee_2Eis__closest @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ty_2Erealax_2Ereal @ ( arr @ A_27a @ bool ) ) ) ) ) ).
thf(tp_c_2Eieee_2Eis__denormal,type,
c_2Eieee_2Eis__denormal: $i ).
thf(mem_c_2Eieee_2Eis__denormal,axiom,
mem @ c_2Eieee_2Eis__denormal @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ).
thf(tp_c_2Eieee_2Eis__double,type,
c_2Eieee_2Eis__double: $i ).
thf(mem_c_2Eieee_2Eis__double,axiom,
mem @ c_2Eieee_2Eis__double @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ bool ) ).
thf(tp_c_2Eieee_2Eis__double__extended,type,
c_2Eieee_2Eis__double__extended: $i ).
thf(mem_c_2Eieee_2Eis__double__extended,axiom,
mem @ c_2Eieee_2Eis__double__extended @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ bool ) ).
thf(tp_c_2Eieee_2Eis__finite,type,
c_2Eieee_2Eis__finite: $i ).
thf(mem_c_2Eieee_2Eis__finite,axiom,
mem @ c_2Eieee_2Eis__finite @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ).
thf(tp_c_2Eieee_2Eis__infinity,type,
c_2Eieee_2Eis__infinity: $i ).
thf(mem_c_2Eieee_2Eis__infinity,axiom,
mem @ c_2Eieee_2Eis__infinity @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ).
thf(tp_c_2Eieee_2Eis__integral,type,
c_2Eieee_2Eis__integral: $i ).
thf(mem_c_2Eieee_2Eis__integral,axiom,
mem @ c_2Eieee_2Eis__integral @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ).
thf(tp_c_2Eieee_2Eis__nan,type,
c_2Eieee_2Eis__nan: $i ).
thf(mem_c_2Eieee_2Eis__nan,axiom,
mem @ c_2Eieee_2Eis__nan @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ).
thf(tp_c_2Eieee_2Eis__normal,type,
c_2Eieee_2Eis__normal: $i ).
thf(mem_c_2Eieee_2Eis__normal,axiom,
mem @ c_2Eieee_2Eis__normal @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ).
thf(tp_c_2Eieee_2Eis__single,type,
c_2Eieee_2Eis__single: $i ).
thf(mem_c_2Eieee_2Eis__single,axiom,
mem @ c_2Eieee_2Eis__single @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ bool ) ).
thf(tp_c_2Eieee_2Eis__single__extended,type,
c_2Eieee_2Eis__single__extended: $i ).
thf(mem_c_2Eieee_2Eis__single__extended,axiom,
mem @ c_2Eieee_2Eis__single__extended @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ bool ) ).
thf(tp_c_2Eieee_2Eis__valid,type,
c_2Eieee_2Eis__valid: $i ).
thf(mem_c_2Eieee_2Eis__valid,axiom,
mem @ c_2Eieee_2Eis__valid @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ).
thf(tp_c_2Eieee_2Eis__zero,type,
c_2Eieee_2Eis__zero: $i ).
thf(mem_c_2Eieee_2Eis__zero,axiom,
mem @ c_2Eieee_2Eis__zero @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) ) ).
thf(tp_c_2Eieee_2Elargest,type,
c_2Eieee_2Elargest: $i ).
thf(mem_c_2Eieee_2Elargest,axiom,
mem @ c_2Eieee_2Elargest @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Erealax_2Ereal ) ).
thf(stp_fo_c_2Eieee_2Elargest,type,
fo__c_2Eieee_2Elargest: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal ).
thf(stp_eq_fo_c_2Eieee_2Elargest,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Eieee_2Elargest @ X0 ) )
= ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Eminus,type,
c_2Eieee_2Eminus: $i ).
thf(mem_c_2Eieee_2Eminus,axiom,
mem @ c_2Eieee_2Eminus @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( 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 ) ) ) ) ).
thf(tp_c_2Eieee_2Eminus__infinity,type,
c_2Eieee_2Eminus__infinity: $i ).
thf(mem_c_2Eieee_2Eminus__infinity,axiom,
mem @ c_2Eieee_2Eminus__infinity @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Eieee_2Eminus__zero,type,
c_2Eieee_2Eminus__zero: $i ).
thf(mem_c_2Eieee_2Eminus__zero,axiom,
mem @ c_2Eieee_2Eminus__zero @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Eieee_2Enum2ccode,type,
c_2Eieee_2Enum2ccode: $i ).
thf(mem_c_2Eieee_2Enum2ccode,axiom,
mem @ c_2Eieee_2Enum2ccode @ ( arr @ ty_2Enum_2Enum @ ty_2Eieee_2Eccode ) ).
thf(stp_fo_c_2Eieee_2Enum2ccode,type,
fo__c_2Eieee_2Enum2ccode: tp__ty_2Enum_2Enum > tp__ty_2Eieee_2Eccode ).
thf(stp_eq_fo_c_2Eieee_2Enum2ccode,axiom,
! [X0: tp__ty_2Enum_2Enum] :
( ( inj__ty_2Eieee_2Eccode @ ( fo__c_2Eieee_2Enum2ccode @ X0 ) )
= ( ap @ c_2Eieee_2Enum2ccode @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Enum2roundmode,type,
c_2Eieee_2Enum2roundmode: $i ).
thf(mem_c_2Eieee_2Enum2roundmode,axiom,
mem @ c_2Eieee_2Enum2roundmode @ ( arr @ ty_2Enum_2Enum @ ty_2Eieee_2Eroundmode ) ).
thf(stp_fo_c_2Eieee_2Enum2roundmode,type,
fo__c_2Eieee_2Enum2roundmode: tp__ty_2Enum_2Enum > tp__ty_2Eieee_2Eroundmode ).
thf(stp_eq_fo_c_2Eieee_2Enum2roundmode,axiom,
! [X0: tp__ty_2Enum_2Enum] :
( ( inj__ty_2Eieee_2Eroundmode @ ( fo__c_2Eieee_2Enum2roundmode @ X0 ) )
= ( ap @ c_2Eieee_2Enum2roundmode @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Eplus__infinity,type,
c_2Eieee_2Eplus__infinity: $i ).
thf(mem_c_2Eieee_2Eplus__infinity,axiom,
mem @ c_2Eieee_2Eplus__infinity @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Eieee_2Eplus__zero,type,
c_2Eieee_2Eplus__zero: $i ).
thf(mem_c_2Eieee_2Eplus__zero,axiom,
mem @ c_2Eieee_2Eplus__zero @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Eieee_2Erem,type,
c_2Eieee_2Erem: $i ).
thf(mem_c_2Eieee_2Erem,axiom,
mem @ c_2Eieee_2Erem @ ( arr @ ty_2Erealax_2Ereal @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) ).
thf(stp_fo_c_2Eieee_2Erem,type,
fo__c_2Eieee_2Erem: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
thf(stp_eq_fo_c_2Eieee_2Erem,axiom,
! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Eieee_2Erem @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Eieee_2Erem @ ( inj__ty_2Erealax_2Ereal @ X0 ) ) @ ( inj__ty_2Erealax_2Ereal @ X1 ) ) ) ).
thf(tp_c_2Eieee_2Eround,type,
c_2Eieee_2Eround: $i ).
thf(mem_c_2Eieee_2Eround,axiom,
mem @ c_2Eieee_2Eround @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ty_2Erealax_2Ereal @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ) ) ).
thf(tp_c_2Eieee_2Eroundmode2num,type,
c_2Eieee_2Eroundmode2num: $i ).
thf(mem_c_2Eieee_2Eroundmode2num,axiom,
mem @ c_2Eieee_2Eroundmode2num @ ( arr @ ty_2Eieee_2Eroundmode @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Eroundmode2num,type,
fo__c_2Eieee_2Eroundmode2num: tp__ty_2Eieee_2Eroundmode > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Eroundmode2num,axiom,
! [X0: tp__ty_2Eieee_2Eroundmode] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Eroundmode2num @ X0 ) )
= ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Eroundmode__CASE,type,
c_2Eieee_2Eroundmode__CASE: del > $i ).
thf(mem_c_2Eieee_2Eroundmode__CASE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eieee_2Eroundmode__CASE @ A_27a ) @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ A_27a @ ( arr @ A_27a @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) ) ) ).
thf(tp_c_2Eieee_2Eroundmode__size,type,
c_2Eieee_2Eroundmode__size: $i ).
thf(mem_c_2Eieee_2Eroundmode__size,axiom,
mem @ c_2Eieee_2Eroundmode__size @ ( arr @ ty_2Eieee_2Eroundmode @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Eroundmode__size,type,
fo__c_2Eieee_2Eroundmode__size: tp__ty_2Eieee_2Eroundmode > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Eroundmode__size,axiom,
! [X0: tp__ty_2Eieee_2Eroundmode] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Eroundmode__size @ X0 ) )
= ( ap @ c_2Eieee_2Eroundmode__size @ ( inj__ty_2Eieee_2Eroundmode @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Esign,type,
c_2Eieee_2Esign: $i ).
thf(mem_c_2Eieee_2Esign,axiom,
mem @ c_2Eieee_2Esign @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Esign,type,
fo__c_2Eieee_2Esign: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Esign,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Esign @ X0 ) )
= ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Esome__nan,type,
c_2Eieee_2Esome__nan: $i ).
thf(mem_c_2Eieee_2Esome__nan,axiom,
mem @ c_2Eieee_2Esome__nan @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Eieee_2Ethreshold,type,
c_2Eieee_2Ethreshold: $i ).
thf(mem_c_2Eieee_2Ethreshold,axiom,
mem @ c_2Eieee_2Ethreshold @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Erealax_2Ereal ) ).
thf(stp_fo_c_2Eieee_2Ethreshold,type,
fo__c_2Eieee_2Ethreshold: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal ).
thf(stp_eq_fo_c_2Eieee_2Ethreshold,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Eieee_2Ethreshold @ X0 ) )
= ( ap @ c_2Eieee_2Ethreshold @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Etopfloat,type,
c_2Eieee_2Etopfloat: $i ).
thf(mem_c_2Eieee_2Etopfloat,axiom,
mem @ c_2Eieee_2Etopfloat @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Eieee_2Eulp,type,
c_2Eieee_2Eulp: $i ).
thf(mem_c_2Eieee_2Eulp,axiom,
mem @ c_2Eieee_2Eulp @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Erealax_2Ereal ) ) ).
thf(stp_fo_c_2Eieee_2Eulp,type,
fo__c_2Eieee_2Eulp: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal ).
thf(stp_eq_fo_c_2Eieee_2Eulp,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,X1: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Eieee_2Eulp @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Eieee_2Eulp @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X1 ) ) ) ).
thf(tp_c_2Eieee_2Evalof,type,
c_2Eieee_2Evalof: $i ).
thf(mem_c_2Eieee_2Evalof,axiom,
mem @ c_2Eieee_2Evalof @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Erealax_2Ereal ) ) ).
thf(stp_fo_c_2Eieee_2Evalof,type,
fo__c_2Eieee_2Evalof: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal ).
thf(stp_eq_fo_c_2Eieee_2Evalof,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,X1: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Eieee_2Evalof @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X1 ) ) ) ).
thf(tp_c_2Eieee_2Ewordlength,type,
c_2Eieee_2Ewordlength: $i ).
thf(mem_c_2Eieee_2Ewordlength,axiom,
mem @ c_2Eieee_2Ewordlength @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Eieee_2Ewordlength,type,
fo__c_2Eieee_2Ewordlength: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Eieee_2Ewordlength,axiom,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eieee_2Ewordlength @ X0 ) )
= ( ap @ c_2Eieee_2Ewordlength @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
thf(tp_c_2Eieee_2Ezerosign,type,
c_2Eieee_2Ezerosign: $i ).
thf(mem_c_2Eieee_2Ezerosign,axiom,
mem @ c_2Eieee_2Ezerosign @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( 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 ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eexpwidth,axiom,
! [V0ew: tp__ty_2Enum_2Enum,V1fw: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eexpwidth @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0ew ) ) @ ( inj__ty_2Enum_2Enum @ V1fw ) ) ) )
= V0ew ) ).
thf(ax_thm_2Eieee_2Efracwidth,axiom,
! [V0ew: tp__ty_2Enum_2Enum,V1fw: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Efracwidth @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0ew ) ) @ ( inj__ty_2Enum_2Enum @ V1fw ) ) ) )
= V1fw ) ).
thf(ax_thm_2Eieee_2Ewordlength,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Ewordlength @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Eieee_2Eexpwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ c_2Eieee_2Efracwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eemax,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( 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 ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Ebias,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Ebias @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( 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_2Eexpwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eis__single,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ c_2Eieee_2Eis__single @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
<=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eexpwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Ewordlength @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( 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(ax_thm_2Eieee_2Eis__double,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ c_2Eieee_2Eis__double @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
<=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eexpwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Ewordlength @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__ty_2Enum_2Enum @ ( 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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eis__single__extended,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ c_2Eieee_2Eis__single__extended @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ c_2Eieee_2Eexpwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ c_2Eieee_2Ewordlength @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eis__double__extended,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ c_2Eieee_2Eis__double__extended @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ c_2Eieee_2Eexpwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( 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_2Earithmetic_2E_3E_3D @ ( ap @ c_2Eieee_2Ewordlength @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Esign,axiom,
! [V0s: tp__ty_2Enum_2Enum,V1e: tp__ty_2Enum_2Enum,V2f: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Esign @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V0s ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1e ) ) @ ( inj__ty_2Enum_2Enum @ V2f ) ) ) ) )
= V0s ) ).
thf(ax_thm_2Eieee_2Eexponent,axiom,
! [V0s: tp__ty_2Enum_2Enum,V1e: tp__ty_2Enum_2Enum,V2f: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eexponent @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V0s ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1e ) ) @ ( inj__ty_2Enum_2Enum @ V2f ) ) ) ) )
= V1e ) ).
thf(ax_thm_2Eieee_2Efraction,axiom,
! [V0s: tp__ty_2Enum_2Enum,V1e: tp__ty_2Enum_2Enum,V2f: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Efraction @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V0s ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1e ) ) @ ( inj__ty_2Enum_2Enum @ V2f ) ) ) ) )
= V2f ) ).
thf(ax_thm_2Eieee_2Eis__nan,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__nan @ ( 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_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 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) )
& ( ( 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 @ V1a ) ) )
!= fo__c_2Enum_2E0 ) ) ) ).
thf(ax_thm_2Eieee_2Eis__infinity,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__infinity @ ( 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_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 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) )
& ( ( 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 @ V1a ) ) )
= fo__c_2Enum_2E0 ) ) ) ).
thf(ax_thm_2Eieee_2Eis__normal,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__normal @ ( 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 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Eieee_2Eexponent @ ( 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_2Eexponent @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eis__denormal,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__denormal @ ( 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_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 ) ) )
= fo__c_2Enum_2E0 )
& ( ( 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 @ V1a ) ) )
!= fo__c_2Enum_2E0 ) ) ) ).
thf(ax_thm_2Eieee_2Eis__zero,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__zero @ ( 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_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 ) ) )
= fo__c_2Enum_2E0 )
& ( ( 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 @ V1a ) ) )
= fo__c_2Enum_2E0 ) ) ) ).
thf(ax_thm_2Eieee_2Eis__valid,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1s: tp__ty_2Enum_2Enum,V2e: tp__ty_2Enum_2Enum,V3f: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__valid @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2e ) ) @ ( inj__ty_2Enum_2Enum @ V3f ) ) ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1s ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2e ) ) @ ( 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 @ ( inj__ty_2Enum_2Enum @ V3f ) ) @ ( 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(ax_thm_2Eieee_2Eis__finite,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__finite @ ( 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_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_2Eieee_2Eis__normal @ ( 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_2Eieee_2Eis__denormal @ ( 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_2Eieee_2Eis__zero @ ( 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 ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eplus__infinity,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eplus__infinity @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eminus__infinity,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eminus__infinity @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eplus__zero,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eplus__zero @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eminus__zero,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eminus__zero @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Etopfloat,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Etopfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( 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 ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Ebottomfloat,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Ebottomfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( 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 ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eminus,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__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Eieee_2Eminus @ ( 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__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( 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_2Epair_2E_2C @ ty_2Enum_2Enum @ 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 ) ) ) @ ( ap @ c_2Eieee_2Efraction @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1a ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eencoding,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1s: tp__ty_2Enum_2Enum,V2e: tp__ty_2Enum_2Enum,V3f: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Eieee_2Eencoding @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2e ) ) @ ( inj__ty_2Enum_2Enum @ V3f ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1s ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( 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_2Ewordlength @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2e ) ) @ ( 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 ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3f ) ) ) ) ).
thf(ax_thm_2Eieee_2Evalof,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1s: tp__ty_2Enum_2Enum,V2e: tp__ty_2Enum_2Enum,V3f: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2e ) ) @ ( inj__ty_2Enum_2Enum @ V3f ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Erealax_2Ereal ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2e ) ) @ ( 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 ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1s ) ) ) @ ( 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 @ ( inj__ty_2Enum_2Enum @ V3f ) ) ) @ ( 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 ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1s ) ) ) @ ( 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 @ V2e ) ) ) @ ( 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 @ ( inj__ty_2Enum_2Enum @ V3f ) ) ) @ ( 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(ax_thm_2Eieee_2Elargest,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( 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 @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( 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_2Eieee_2Ebias @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( 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 @ c_2Eieee_2Efracwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Ethreshold,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2Ethreshold @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( 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 @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Eieee_2Eemax @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( 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_2Eieee_2Ebias @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ c_2Ereal_2Ereal__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( 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 @ c_2Enum_2ESUC @ ( ap @ c_2Eieee_2Efracwidth @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eulp,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_2Eulp @ ( 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 @ c_2Ereal_2Ereal__sub @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ 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 ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ 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 ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eroundmode__TY__DEF,axiom,
? [V0rep: $i] :
( ( mem @ V0rep @ ( arr @ ty_2Eieee_2Eroundmode @ ty_2Enum_2Enum ) )
& ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ty_2Enum_2Enum @ ty_2Eieee_2Eroundmode )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1n: $i] : ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V1n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
@ V0rep ) ) ) ).
thf(ax_thm_2Eieee_2Eroundmode__BIJ,axiom,
( ! [V0a: tp__ty_2Eieee_2Eroundmode] :
( ( surj__ty_2Eieee_2Eroundmode @ ( ap @ c_2Eieee_2Enum2roundmode @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ V0a ) ) ) )
= V0a )
& ! [V1r: tp__ty_2Enum_2Enum] :
( ( p
@ ( ap
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V2n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1r ) ) )
<=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( ap @ c_2Eieee_2Enum2roundmode @ ( inj__ty_2Enum_2Enum @ V1r ) ) ) )
= V1r ) ) ) ).
thf(conj_thm_2Eieee_2Enum2roundmode__roundmode2num,axiom,
! [V0a: tp__ty_2Eieee_2Eroundmode] :
( ( surj__ty_2Eieee_2Eroundmode @ ( ap @ c_2Eieee_2Enum2roundmode @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ V0a ) ) ) )
= V0a ) ).
thf(conj_thm_2Eieee_2Eroundmode2num__num2roundmode,axiom,
! [V0r: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( ap @ c_2Eieee_2Enum2roundmode @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) )
= V0r ) ) ).
thf(conj_thm_2Eieee_2Enum2roundmode__11,axiom,
! [V0r: tp__ty_2Enum_2Enum,V1r_27: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1r_27 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
=> ( ( ( surj__ty_2Eieee_2Eroundmode @ ( ap @ c_2Eieee_2Enum2roundmode @ ( inj__ty_2Enum_2Enum @ V0r ) ) )
= ( surj__ty_2Eieee_2Eroundmode @ ( ap @ c_2Eieee_2Enum2roundmode @ ( inj__ty_2Enum_2Enum @ V1r_27 ) ) ) )
<=> ( V0r = V1r_27 ) ) ) ) ).
thf(conj_thm_2Eieee_2Eroundmode2num__11,axiom,
! [V0a: tp__ty_2Eieee_2Eroundmode,V1a_27: tp__ty_2Eieee_2Eroundmode] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ V0a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ V1a_27 ) ) ) )
<=> ( V0a = V1a_27 ) ) ).
thf(conj_thm_2Eieee_2Enum2roundmode__ONTO,axiom,
! [V0a: tp__ty_2Eieee_2Eroundmode] :
? [V1r: tp__ty_2Enum_2Enum] :
( ( V0a
= ( surj__ty_2Eieee_2Eroundmode @ ( ap @ c_2Eieee_2Enum2roundmode @ ( inj__ty_2Enum_2Enum @ V1r ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1r ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eroundmode2num__ONTO,axiom,
! [V0r: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ? [V1a: tp__ty_2Eieee_2Eroundmode] :
( V0r
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ V1a ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Enum2roundmode__thm,axiom,
( ( ( surj__ty_2Eieee_2Eroundmode @ ( ap @ c_2Eieee_2Enum2roundmode @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= fo__c_2Eieee_2ETo__nearest )
& ( ( surj__ty_2Eieee_2Eroundmode @ ( ap @ c_2Eieee_2Enum2roundmode @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= fo__c_2Eieee_2Efloat__To__zero )
& ( ( surj__ty_2Eieee_2Eroundmode @ ( ap @ c_2Eieee_2Enum2roundmode @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= fo__c_2Eieee_2ETo__pinfinity )
& ( ( surj__ty_2Eieee_2Eroundmode @ ( ap @ c_2Eieee_2Enum2roundmode @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= fo__c_2Eieee_2ETo__ninfinity ) ) ).
thf(conj_thm_2Eieee_2Eroundmode2num__thm,axiom,
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) )
= fo__c_2Enum_2E0 )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2Efloat__To__zero ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__pinfinity ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__ninfinity ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eroundmode__EQ__roundmode,axiom,
! [V0a: tp__ty_2Eieee_2Eroundmode,V1a_27: tp__ty_2Eieee_2Eroundmode] :
( ( V0a = V1a_27 )
<=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ V0a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ V1a_27 ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eroundmode__size__def,axiom,
! [V0x: tp__ty_2Eieee_2Eroundmode] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eroundmode__size @ ( inj__ty_2Eieee_2Eroundmode @ V0x ) ) )
= fo__c_2Enum_2E0 ) ).
thf(ax_thm_2Eieee_2Eroundmode__CASE,axiom,
! [A_27a: del,V0x: tp__ty_2Eieee_2Eroundmode,V1v0: $i] :
( ( mem @ V1v0 @ A_27a )
=> ! [V2v1: $i] :
( ( mem @ V2v1 @ A_27a )
=> ! [V3v2: $i] :
( ( mem @ V3v2 @ A_27a )
=> ! [V4v3: $i] :
( ( mem @ V4v3 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eroundmode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eroundmode @ V0x ) ) @ V1v0 ) @ V2v1 ) @ V3v2 ) @ V4v3 )
= ( ap
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5m: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V5m ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V1v0 ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V5m ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V2v1 ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V5m ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V3v2 ) @ V4v3 ) ) ) )
@ ( ap @ c_2Eieee_2Eroundmode2num @ ( inj__ty_2Eieee_2Eroundmode @ V0x ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eroundmode__case__def,axiom,
! [A_27a: del] :
( ! [V0v0: $i] :
( ( mem @ V0v0 @ A_27a )
=> ! [V1v1: $i] :
( ( mem @ V1v1 @ A_27a )
=> ! [V2v2: $i] :
( ( mem @ V2v2 @ A_27a )
=> ! [V3v3: $i] :
( ( mem @ V3v3 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eroundmode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ V0v0 ) @ V1v1 ) @ V2v2 ) @ V3v3 )
= V0v0 ) ) ) ) )
& ! [V4v0: $i] :
( ( mem @ V4v0 @ A_27a )
=> ! [V5v1: $i] :
( ( mem @ V5v1 @ A_27a )
=> ! [V6v2: $i] :
( ( mem @ V6v2 @ A_27a )
=> ! [V7v3: $i] :
( ( mem @ V7v3 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eroundmode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2Efloat__To__zero ) ) @ V4v0 ) @ V5v1 ) @ V6v2 ) @ V7v3 )
= V5v1 ) ) ) ) )
& ! [V8v0: $i] :
( ( mem @ V8v0 @ A_27a )
=> ! [V9v1: $i] :
( ( mem @ V9v1 @ A_27a )
=> ! [V10v2: $i] :
( ( mem @ V10v2 @ A_27a )
=> ! [V11v3: $i] :
( ( mem @ V11v3 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eroundmode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__pinfinity ) ) @ V8v0 ) @ V9v1 ) @ V10v2 ) @ V11v3 )
= V10v2 ) ) ) ) )
& ! [V12v0: $i] :
( ( mem @ V12v0 @ A_27a )
=> ! [V13v1: $i] :
( ( mem @ V13v1 @ A_27a )
=> ! [V14v2: $i] :
( ( mem @ V14v2 @ A_27a )
=> ! [V15v3: $i] :
( ( mem @ V15v3 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eroundmode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__ninfinity ) ) @ V12v0 ) @ V13v1 ) @ V14v2 ) @ V15v3 )
= V15v3 ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Edatatype__roundmode,axiom,
! [V0roundmode: $i] :
( ( mem @ V0roundmode @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ty_2Eieee_2Eroundmode @ ( arr @ ty_2Eieee_2Eroundmode @ bool ) ) ) ) )
=> ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ bool ) @ ( ap @ ( ap @ ( ap @ ( ap @ V0roundmode @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2Efloat__To__zero ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__pinfinity ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__ninfinity ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eroundmode__distinct,axiom,
( ( fo__c_2Eieee_2ETo__nearest != fo__c_2Eieee_2Efloat__To__zero )
& ( fo__c_2Eieee_2ETo__nearest != fo__c_2Eieee_2ETo__pinfinity )
& ( fo__c_2Eieee_2ETo__nearest != fo__c_2Eieee_2ETo__ninfinity )
& ( fo__c_2Eieee_2Efloat__To__zero != fo__c_2Eieee_2ETo__pinfinity )
& ( fo__c_2Eieee_2Efloat__To__zero != fo__c_2Eieee_2ETo__ninfinity )
& ( fo__c_2Eieee_2ETo__pinfinity != fo__c_2Eieee_2ETo__ninfinity ) ) ).
thf(conj_thm_2Eieee_2Eroundmode__nchotomy,axiom,
! [V0a: tp__ty_2Eieee_2Eroundmode] :
( ( V0a = fo__c_2Eieee_2ETo__nearest )
| ( V0a = fo__c_2Eieee_2Efloat__To__zero )
| ( V0a = fo__c_2Eieee_2ETo__pinfinity )
| ( V0a = fo__c_2Eieee_2ETo__ninfinity ) ) ).
thf(conj_thm_2Eieee_2Eroundmode__Axiom,axiom,
! [A_27a: del,V0x0: $i] :
( ( mem @ V0x0 @ A_27a )
=> ! [V1x1: $i] :
( ( mem @ V1x1 @ A_27a )
=> ! [V2x2: $i] :
( ( mem @ V2x2 @ A_27a )
=> ! [V3x3: $i] :
( ( mem @ V3x3 @ A_27a )
=> ? [V4f: $i] :
( ( mem @ V4f @ ( arr @ ty_2Eieee_2Eroundmode @ A_27a ) )
& ( ( ap @ V4f @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) )
= V0x0 )
& ( ( ap @ V4f @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2Efloat__To__zero ) )
= V1x1 )
& ( ( ap @ V4f @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__pinfinity ) )
= V2x2 )
& ( ( ap @ V4f @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__ninfinity ) )
= V3x3 ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eroundmode__induction,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Eieee_2Eroundmode @ bool ) )
=> ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) )
& ( p @ ( ap @ V0P @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__ninfinity ) ) )
& ( p @ ( ap @ V0P @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__pinfinity ) ) )
& ( p @ ( ap @ V0P @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2Efloat__To__zero ) ) ) )
=> ! [V1a: tp__ty_2Eieee_2Eroundmode] : ( p @ ( ap @ V0P @ ( inj__ty_2Eieee_2Eroundmode @ V1a ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eroundmode__case__cong,axiom,
! [A_27a: del,V0v0_27: $i] :
( ( mem @ V0v0_27 @ A_27a )
=> ! [V1v1_27: $i] :
( ( mem @ V1v1_27 @ A_27a )
=> ! [V2v2_27: $i] :
( ( mem @ V2v2_27 @ A_27a )
=> ! [V3v3_27: $i] :
( ( mem @ V3v3_27 @ A_27a )
=> ! [V4M: tp__ty_2Eieee_2Eroundmode,V5M_27: tp__ty_2Eieee_2Eroundmode,V6v0: $i] :
( ( mem @ V6v0 @ A_27a )
=> ! [V7v1: $i] :
( ( mem @ V7v1 @ A_27a )
=> ! [V8v2: $i] :
( ( mem @ V8v2 @ A_27a )
=> ! [V9v3: $i] :
( ( mem @ V9v3 @ A_27a )
=> ( ( ( V4M = V5M_27 )
& ( ( V5M_27 = fo__c_2Eieee_2ETo__nearest )
=> ( V6v0 = V0v0_27 ) )
& ( ( V5M_27 = fo__c_2Eieee_2Efloat__To__zero )
=> ( V7v1 = V1v1_27 ) )
& ( ( V5M_27 = fo__c_2Eieee_2ETo__pinfinity )
=> ( V8v2 = V2v2_27 ) )
& ( ( V5M_27 = fo__c_2Eieee_2ETo__ninfinity )
=> ( V9v3 = V3v3_27 ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eroundmode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eroundmode @ V4M ) ) @ V6v0 ) @ V7v1 ) @ V8v2 ) @ V9v3 )
= ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eroundmode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eroundmode @ V5M_27 ) ) @ V0v0_27 ) @ V1v1_27 ) @ V2v2_27 ) @ V3v3_27 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eroundmode__case__eq,axiom,
! [A_27a: del,V0x: tp__ty_2Eieee_2Eroundmode,V1v0: $i] :
( ( mem @ V1v0 @ A_27a )
=> ! [V2v1: $i] :
( ( mem @ V2v1 @ A_27a )
=> ! [V3v2: $i] :
( ( mem @ V3v2 @ A_27a )
=> ! [V4v3: $i] :
( ( mem @ V4v3 @ A_27a )
=> ! [V5v: $i] :
( ( mem @ V5v @ A_27a )
=> ( ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eroundmode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eroundmode @ V0x ) ) @ V1v0 ) @ V2v1 ) @ V3v2 ) @ V4v3 )
= V5v )
<=> ( ( ( V0x = fo__c_2Eieee_2ETo__nearest )
& ( V1v0 = V5v ) )
| ( ( V0x = fo__c_2Eieee_2Efloat__To__zero )
& ( V2v1 = V5v ) )
| ( ( V0x = fo__c_2Eieee_2ETo__pinfinity )
& ( V3v2 = V5v ) )
| ( ( V0x = fo__c_2Eieee_2ETo__ninfinity )
& ( V4v3 = V5v ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eis__closest,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
=> ! [V1s: $i] :
( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
=> ! [V2x: tp__ty_2Erealax_2Ereal,V3a: $i] :
( ( mem @ V3a @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eis__closest @ A_27a ) @ V0v ) @ V1s ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) @ V3a ) )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3a ) @ V1s ) )
& ! [V4b: $i] :
( ( mem @ V4b @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4b ) @ V1s ) )
=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0v @ V3a ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) ) @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( ap @ V0v @ V4b ) ) @ ( inj__ty_2Erealax_2Ereal @ V2x ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eclosest,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( arr @ A_27a @ ty_2Erealax_2Ereal ) )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27a @ bool ) )
=> ! [V2s: $i] :
( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
=> ! [V3x: tp__ty_2Erealax_2Ereal] :
( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ A_27a ) @ V0v ) @ V1p ) @ V2s ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) )
= ( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V4a: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eis__closest @ A_27a ) @ V0v ) @ V2s ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V4a ) )
@ ( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V5b: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eis__closest @ A_27a ) @ V0v ) @ V2s ) @ ( inj__ty_2Erealax_2Ereal @ V3x ) ) @ V5b ) ) @ ( ap @ V1p @ V5b ) ) ) ) )
@ ( ap @ V1p @ V4a ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eround__def,axiom,
( ! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( 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 ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ c_2Eieee_2Ethreshold @ ( 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 ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( ap @ c_2Eieee_2Ethreshold @ ( 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 ) ) )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V2a: $i] : ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ c_2Eieee_2Efraction @ V2a ) ) ) )
@ ( 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 ) )
@ ^ [V3a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V3a ) @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ V3a ) ) ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) ) ) )
& ! [V4X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V5x: tp__ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V4X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2Efloat__To__zero ) ) @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V4X ) ) ) ) ) @ ( ap @ c_2Eieee_2Ebottomfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V4X ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__gt @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V4X ) ) ) ) @ ( ap @ c_2Eieee_2Etopfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V4X ) ) )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V4X ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V6x: $i] : c_2Ebool_2ET ) )
@ ( 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 ) )
@ ^ [V7a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V7a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V4X ) ) @ V7a ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V4X ) ) @ V7a ) ) ) @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V5x ) ) ) ) ) ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V5x ) ) ) ) ) )
& ! [V8X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V9x: tp__ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V8X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__pinfinity ) ) @ ( inj__ty_2Erealax_2Ereal @ V9x ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V9x ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V8X ) ) ) ) ) @ ( ap @ c_2Eieee_2Ebottomfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V8X ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__gt @ ( inj__ty_2Erealax_2Ereal @ V9x ) ) @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V8X ) ) ) ) @ ( ap @ c_2Eieee_2Eplus__infinity @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V8X ) ) )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V8X ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V10x: $i] : c_2Ebool_2ET ) )
@ ( 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 ) )
@ ^ [V11a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V11a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V8X ) ) @ V11a ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V8X ) ) @ V11a ) ) @ ( inj__ty_2Erealax_2Ereal @ V9x ) ) ) ) ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V9x ) ) ) ) ) )
& ! [V12X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V13x: tp__ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V12X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__ninfinity ) ) @ ( inj__ty_2Erealax_2Ereal @ V13x ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V13x ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V12X ) ) ) ) ) @ ( ap @ c_2Eieee_2Eminus__infinity @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V12X ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__gt @ ( inj__ty_2Erealax_2Ereal @ V13x ) ) @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V12X ) ) ) ) @ ( ap @ c_2Eieee_2Etopfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V12X ) ) )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V12X ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V14x: $i] : c_2Ebool_2ET ) )
@ ( 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 ) )
@ ^ [V15a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V15a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__finite @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V12X ) ) @ V15a ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V12X ) ) @ V15a ) ) @ ( inj__ty_2Erealax_2Ereal @ V13x ) ) ) ) ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V13x ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eis__integral,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__integral @ ( 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_2Eieee_2Eis__finite @ ( 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 ) ) )
& ? [V2n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Ereal_2Eabs @ ( 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 @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eintround__def,axiom,
( ! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1x: tp__ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eintround @ ( 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 ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ c_2Eieee_2Ethreshold @ ( 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 ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( inj__ty_2Erealax_2Ereal @ V1x ) ) @ ( ap @ c_2Eieee_2Ethreshold @ ( 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 ) ) )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V2a: $i] :
( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3n: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Earithmetic_2EEVEN @ V3n ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal ) @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ V2a ) ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ V3n ) ) ) ) ) ) )
@ ( 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__integral @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ V4a ) ) ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V1x ) ) ) ) ) )
& ! [V5X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V6x: tp__ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eintround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V5X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2Efloat__To__zero ) ) @ ( inj__ty_2Erealax_2Ereal @ V6x ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V6x ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V5X ) ) ) ) ) @ ( ap @ c_2Eieee_2Ebottomfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V5X ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__gt @ ( inj__ty_2Erealax_2Ereal @ V6x ) ) @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V5X ) ) ) ) @ ( ap @ c_2Eieee_2Etopfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V5X ) ) )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V5X ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V7x: $i] : c_2Ebool_2ET ) )
@ ( 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 ) )
@ ^ [V8a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V8a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__integral @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V5X ) ) @ V8a ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Eabs @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V5X ) ) @ V8a ) ) ) @ ( ap @ c_2Ereal_2Eabs @ ( inj__ty_2Erealax_2Ereal @ V6x ) ) ) ) ) ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V6x ) ) ) ) ) )
& ! [V9X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V10x: tp__ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eintround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V9X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__pinfinity ) ) @ ( inj__ty_2Erealax_2Ereal @ V10x ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V10x ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V9X ) ) ) ) ) @ ( ap @ c_2Eieee_2Ebottomfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V9X ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__gt @ ( inj__ty_2Erealax_2Ereal @ V10x ) ) @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V9X ) ) ) ) @ ( ap @ c_2Eieee_2Eplus__infinity @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V9X ) ) )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V9X ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V11x: $i] : c_2Ebool_2ET ) )
@ ( 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 ) )
@ ^ [V12a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V12a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__integral @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V9X ) ) @ V12a ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__ge @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V9X ) ) @ V12a ) ) @ ( inj__ty_2Erealax_2Ereal @ V10x ) ) ) ) ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V10x ) ) ) ) ) )
& ! [V13X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V14x: tp__ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eintround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V13X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__ninfinity ) ) @ ( inj__ty_2Erealax_2Ereal @ V14x ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V14x ) ) @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V13X ) ) ) ) ) @ ( ap @ c_2Eieee_2Eminus__infinity @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V13X ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__gt @ ( inj__ty_2Erealax_2Ereal @ V14x ) ) @ ( ap @ c_2Eieee_2Elargest @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V13X ) ) ) ) @ ( ap @ c_2Eieee_2Etopfloat @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V13X ) ) )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V13X ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
@ ^ [V15x: $i] : c_2Ebool_2ET ) )
@ ( 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 ) )
@ ^ [V16a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ V16a ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__integral @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V13X ) ) @ V16a ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ ( ap @ c_2Eieee_2Evalof @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V13X ) ) @ V16a ) ) @ ( inj__ty_2Erealax_2Ereal @ V14x ) ) ) ) ) ) )
@ ( inj__ty_2Erealax_2Ereal @ V14x ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Esome__nan,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Esome__nan @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
@ ( ap @ ( c_2Emin_2E_40 @ ( 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_2Eieee_2Eis__nan @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ V1a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Ezerosign,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1s: tp__ty_2Enum_2Enum,V2a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Enum_2Enum @ V1s ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1s ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Eieee_2Eplus__zero @ ( 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 ) ) ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) ) ) ).
thf(ax_thm_2Eieee_2Erem,axiom,
! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Eieee_2Erem @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
= ( surj__ty_2Erealax_2Ereal
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V2n: $i] : ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ V2n ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) ) )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2Eieee_2Eclosest @ ty_2Erealax_2Ereal ) @ ( c_2Ecombin_2EI @ ty_2Erealax_2Ereal ) )
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V3x: $i] :
( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4n: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Earithmetic_2EEVEN @ V4n ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal ) @ ( ap @ c_2Ereal_2Eabs @ V3x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ V4n ) ) ) ) ) ) )
@ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal )
@ ( lam @ ty_2Erealax_2Ereal
@ ^ [V5x: $i] :
( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ bool ) @ V5x )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6n: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Erealax_2Ereal ) @ ( ap @ c_2Ereal_2Eabs @ V5x ) ) @ ( ap @ c_2Ereal_2Ereal__of__num @ V6n ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efintrnd,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1m: tp__ty_2Eieee_2Eroundmode,V2a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efintrnd @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esome__nan @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eintround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( 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 @ V2a ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efadd,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1m: tp__ty_2Eieee_2Eroundmode,V2a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V3b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efadd @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V3b ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V3b ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) ) ) ) ) ) ) ) @ ( ap @ c_2Eieee_2Esome__nan @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V3b ) ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V3b ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) ) ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Eieee_2Eroundmode ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__ninfinity ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__add @ ( 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 @ V2a ) ) ) @ ( 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 @ V3b ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efsub,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1m: tp__ty_2Eieee_2Eroundmode,V2a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V3b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efsub @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V3b ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V3b ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) ) ) ) ) ) ) @ ( ap @ c_2Eieee_2Esome__nan @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V3b ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eminus @ ( 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 @ V3b ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V3b ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) ) ) ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Eieee_2Eroundmode ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__ninfinity ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( ap @ ( ap @ c_2Ereal_2Ereal__sub @ ( 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 @ V2a ) ) ) @ ( 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 @ V3b ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efmul,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1m: tp__ty_2Eieee_2Eroundmode,V2a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V3b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efmul @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V3b ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V3b ) ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V3b ) ) ) ) ) ) ) @ ( ap @ c_2Eieee_2Esome__nan @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V3b ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) ) ) @ ( ap @ c_2Eieee_2Eplus__infinity @ ( 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 ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__mul @ ( 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 @ V2a ) ) ) @ ( 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 @ V3b ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efdiv,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1m: tp__ty_2Eieee_2Eroundmode,V2a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V3b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efdiv @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V3b ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V3b ) ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V3b ) ) ) ) ) ) ) @ ( ap @ c_2Eieee_2Esome__nan @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V3b ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) ) ) @ ( ap @ c_2Eieee_2Eplus__infinity @ ( 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 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V3b ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) ) ) @ ( ap @ c_2Eieee_2Eplus__zero @ ( 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 ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( ap @ ( ap @ c_2Ereal_2E_2F @ ( 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 @ V2a ) ) ) @ ( 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 @ V3b ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efsqrt,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1m: tp__ty_2Eieee_2Eroundmode,V2a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efsqrt @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Esome__nan @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Eieee_2Esome__nan @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( ap @ c_2Etransc_2Esqrt @ ( 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 @ V2a ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efrem,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1m: tp__ty_2Eieee_2Eroundmode,V2a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V3b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efrem @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V3b ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V3b ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2a ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ ( 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 @ V3b ) ) ) ) ) ) @ ( ap @ c_2Eieee_2Esome__nan @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V3b ) ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Ezerosign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( ap @ c_2Eieee_2Esign @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eround @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( ap @ ( ap @ c_2Eieee_2Erem @ ( 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 @ V2a ) ) ) @ ( 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 @ V3b ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efneg,axiom,
! [V0X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,V1m: tp__ty_2Eieee_2Eroundmode,V2a: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efneg @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X ) ) @ ( inj__ty_2Eieee_2Eroundmode @ V1m ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( 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 @ V2a ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ 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 @ V2a ) ) ) @ ( ap @ c_2Eieee_2Efraction @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2a ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eccode__TY__DEF,axiom,
? [V0rep: $i] :
( ( mem @ V0rep @ ( arr @ ty_2Eieee_2Eccode @ ty_2Enum_2Enum ) )
& ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ty_2Enum_2Enum @ ty_2Eieee_2Eccode )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1n: $i] : ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V1n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
@ V0rep ) ) ) ).
thf(ax_thm_2Eieee_2Eccode__BIJ,axiom,
( ! [V0a: tp__ty_2Eieee_2Eccode] :
( ( surj__ty_2Eieee_2Eccode @ ( ap @ c_2Eieee_2Enum2ccode @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ V0a ) ) ) )
= V0a )
& ! [V1r: tp__ty_2Enum_2Enum] :
( ( p
@ ( ap
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V2n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1r ) ) )
<=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( ap @ c_2Eieee_2Enum2ccode @ ( inj__ty_2Enum_2Enum @ V1r ) ) ) )
= V1r ) ) ) ).
thf(conj_thm_2Eieee_2Enum2ccode__ccode2num,axiom,
! [V0a: tp__ty_2Eieee_2Eccode] :
( ( surj__ty_2Eieee_2Eccode @ ( ap @ c_2Eieee_2Enum2ccode @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ V0a ) ) ) )
= V0a ) ).
thf(conj_thm_2Eieee_2Eccode2num__num2ccode,axiom,
! [V0r: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( ap @ c_2Eieee_2Enum2ccode @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) )
= V0r ) ) ).
thf(conj_thm_2Eieee_2Enum2ccode__11,axiom,
! [V0r: tp__ty_2Enum_2Enum,V1r_27: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1r_27 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
=> ( ( ( surj__ty_2Eieee_2Eccode @ ( ap @ c_2Eieee_2Enum2ccode @ ( inj__ty_2Enum_2Enum @ V0r ) ) )
= ( surj__ty_2Eieee_2Eccode @ ( ap @ c_2Eieee_2Enum2ccode @ ( inj__ty_2Enum_2Enum @ V1r_27 ) ) ) )
<=> ( V0r = V1r_27 ) ) ) ) ).
thf(conj_thm_2Eieee_2Eccode2num__11,axiom,
! [V0a: tp__ty_2Eieee_2Eccode,V1a_27: tp__ty_2Eieee_2Eccode] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ V0a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ V1a_27 ) ) ) )
<=> ( V0a = V1a_27 ) ) ).
thf(conj_thm_2Eieee_2Enum2ccode__ONTO,axiom,
! [V0a: tp__ty_2Eieee_2Eccode] :
? [V1r: tp__ty_2Enum_2Enum] :
( ( V0a
= ( surj__ty_2Eieee_2Eccode @ ( ap @ c_2Eieee_2Enum2ccode @ ( inj__ty_2Enum_2Enum @ V1r ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1r ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eccode2num__ONTO,axiom,
! [V0r: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ? [V1a: tp__ty_2Eieee_2Eccode] :
( V0r
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ V1a ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Enum2ccode__thm,axiom,
( ( ( surj__ty_2Eieee_2Eccode @ ( ap @ c_2Eieee_2Enum2ccode @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= fo__c_2Eieee_2EGt )
& ( ( surj__ty_2Eieee_2Eccode @ ( ap @ c_2Eieee_2Enum2ccode @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= fo__c_2Eieee_2ELt )
& ( ( surj__ty_2Eieee_2Eccode @ ( ap @ c_2Eieee_2Enum2ccode @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= fo__c_2Eieee_2EEq )
& ( ( surj__ty_2Eieee_2Eccode @ ( ap @ c_2Eieee_2Enum2ccode @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= fo__c_2Eieee_2EUn ) ) ).
thf(conj_thm_2Eieee_2Eccode2num__thm,axiom,
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EGt ) ) )
= fo__c_2Enum_2E0 )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2ELt ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EEq ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EUn ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eccode__EQ__ccode,axiom,
! [V0a: tp__ty_2Eieee_2Eccode,V1a_27: tp__ty_2Eieee_2Eccode] :
( ( V0a = V1a_27 )
<=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ V0a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ V1a_27 ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eccode__size__def,axiom,
! [V0x: tp__ty_2Eieee_2Eccode] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eccode__size @ ( inj__ty_2Eieee_2Eccode @ V0x ) ) )
= fo__c_2Enum_2E0 ) ).
thf(ax_thm_2Eieee_2Eccode__CASE,axiom,
! [A_27a: del,V0x: tp__ty_2Eieee_2Eccode,V1v0: $i] :
( ( mem @ V1v0 @ A_27a )
=> ! [V2v1: $i] :
( ( mem @ V2v1 @ A_27a )
=> ! [V3v2: $i] :
( ( mem @ V3v2 @ A_27a )
=> ! [V4v3: $i] :
( ( mem @ V4v3 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eccode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eccode @ V0x ) ) @ V1v0 ) @ V2v1 ) @ V3v2 ) @ V4v3 )
= ( ap
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5m: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V5m ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V1v0 ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V5m ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V2v1 ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V5m ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V3v2 ) @ V4v3 ) ) ) )
@ ( ap @ c_2Eieee_2Eccode2num @ ( inj__ty_2Eieee_2Eccode @ V0x ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eccode__case__def,axiom,
! [A_27a: del] :
( ! [V0v0: $i] :
( ( mem @ V0v0 @ A_27a )
=> ! [V1v1: $i] :
( ( mem @ V1v1 @ A_27a )
=> ! [V2v2: $i] :
( ( mem @ V2v2 @ A_27a )
=> ! [V3v3: $i] :
( ( mem @ V3v3 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eccode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EGt ) ) @ V0v0 ) @ V1v1 ) @ V2v2 ) @ V3v3 )
= V0v0 ) ) ) ) )
& ! [V4v0: $i] :
( ( mem @ V4v0 @ A_27a )
=> ! [V5v1: $i] :
( ( mem @ V5v1 @ A_27a )
=> ! [V6v2: $i] :
( ( mem @ V6v2 @ A_27a )
=> ! [V7v3: $i] :
( ( mem @ V7v3 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eccode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2ELt ) ) @ V4v0 ) @ V5v1 ) @ V6v2 ) @ V7v3 )
= V5v1 ) ) ) ) )
& ! [V8v0: $i] :
( ( mem @ V8v0 @ A_27a )
=> ! [V9v1: $i] :
( ( mem @ V9v1 @ A_27a )
=> ! [V10v2: $i] :
( ( mem @ V10v2 @ A_27a )
=> ! [V11v3: $i] :
( ( mem @ V11v3 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eccode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EEq ) ) @ V8v0 ) @ V9v1 ) @ V10v2 ) @ V11v3 )
= V10v2 ) ) ) ) )
& ! [V12v0: $i] :
( ( mem @ V12v0 @ A_27a )
=> ! [V13v1: $i] :
( ( mem @ V13v1 @ A_27a )
=> ! [V14v2: $i] :
( ( mem @ V14v2 @ A_27a )
=> ! [V15v3: $i] :
( ( mem @ V15v3 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eccode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EUn ) ) @ V12v0 ) @ V13v1 ) @ V14v2 ) @ V15v3 )
= V15v3 ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Edatatype__ccode,axiom,
! [V0ccode: $i] :
( ( mem @ V0ccode @ ( arr @ ty_2Eieee_2Eccode @ ( arr @ ty_2Eieee_2Eccode @ ( arr @ ty_2Eieee_2Eccode @ ( arr @ ty_2Eieee_2Eccode @ bool ) ) ) ) )
=> ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ bool ) @ ( ap @ ( ap @ ( ap @ ( ap @ V0ccode @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EGt ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2ELt ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EEq ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EUn ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eccode__distinct,axiom,
( ( fo__c_2Eieee_2EGt != fo__c_2Eieee_2ELt )
& ( fo__c_2Eieee_2EGt != fo__c_2Eieee_2EEq )
& ( fo__c_2Eieee_2EGt != fo__c_2Eieee_2EUn )
& ( fo__c_2Eieee_2ELt != fo__c_2Eieee_2EEq )
& ( fo__c_2Eieee_2ELt != fo__c_2Eieee_2EUn )
& ( fo__c_2Eieee_2EEq != fo__c_2Eieee_2EUn ) ) ).
thf(conj_thm_2Eieee_2Eccode__nchotomy,axiom,
! [V0a: tp__ty_2Eieee_2Eccode] :
( ( V0a = fo__c_2Eieee_2EGt )
| ( V0a = fo__c_2Eieee_2ELt )
| ( V0a = fo__c_2Eieee_2EEq )
| ( V0a = fo__c_2Eieee_2EUn ) ) ).
thf(conj_thm_2Eieee_2Eccode__Axiom,axiom,
! [A_27a: del,V0x0: $i] :
( ( mem @ V0x0 @ A_27a )
=> ! [V1x1: $i] :
( ( mem @ V1x1 @ A_27a )
=> ! [V2x2: $i] :
( ( mem @ V2x2 @ A_27a )
=> ! [V3x3: $i] :
( ( mem @ V3x3 @ A_27a )
=> ? [V4f: $i] :
( ( mem @ V4f @ ( arr @ ty_2Eieee_2Eccode @ A_27a ) )
& ( ( ap @ V4f @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EGt ) )
= V0x0 )
& ( ( ap @ V4f @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2ELt ) )
= V1x1 )
& ( ( ap @ V4f @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EEq ) )
= V2x2 )
& ( ( ap @ V4f @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EUn ) )
= V3x3 ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eccode__induction,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Eieee_2Eccode @ bool ) )
=> ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EEq ) ) )
& ( p @ ( ap @ V0P @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EGt ) ) )
& ( p @ ( ap @ V0P @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2ELt ) ) )
& ( p @ ( ap @ V0P @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EUn ) ) ) )
=> ! [V1a: tp__ty_2Eieee_2Eccode] : ( p @ ( ap @ V0P @ ( inj__ty_2Eieee_2Eccode @ V1a ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eccode__case__cong,axiom,
! [A_27a: del,V0v0_27: $i] :
( ( mem @ V0v0_27 @ A_27a )
=> ! [V1v1_27: $i] :
( ( mem @ V1v1_27 @ A_27a )
=> ! [V2v2_27: $i] :
( ( mem @ V2v2_27 @ A_27a )
=> ! [V3v3_27: $i] :
( ( mem @ V3v3_27 @ A_27a )
=> ! [V4M: tp__ty_2Eieee_2Eccode,V5M_27: tp__ty_2Eieee_2Eccode,V6v0: $i] :
( ( mem @ V6v0 @ A_27a )
=> ! [V7v1: $i] :
( ( mem @ V7v1 @ A_27a )
=> ! [V8v2: $i] :
( ( mem @ V8v2 @ A_27a )
=> ! [V9v3: $i] :
( ( mem @ V9v3 @ A_27a )
=> ( ( ( V4M = V5M_27 )
& ( ( V5M_27 = fo__c_2Eieee_2EGt )
=> ( V6v0 = V0v0_27 ) )
& ( ( V5M_27 = fo__c_2Eieee_2ELt )
=> ( V7v1 = V1v1_27 ) )
& ( ( V5M_27 = fo__c_2Eieee_2EEq )
=> ( V8v2 = V2v2_27 ) )
& ( ( V5M_27 = fo__c_2Eieee_2EUn )
=> ( V9v3 = V3v3_27 ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eccode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eccode @ V4M ) ) @ V6v0 ) @ V7v1 ) @ V8v2 ) @ V9v3 )
= ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eccode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eccode @ V5M_27 ) ) @ V0v0_27 ) @ V1v1_27 ) @ V2v2_27 ) @ V3v3_27 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Eieee_2Eccode__case__eq,axiom,
! [A_27a: del,V0x: tp__ty_2Eieee_2Eccode,V1v0: $i] :
( ( mem @ V1v0 @ A_27a )
=> ! [V2v1: $i] :
( ( mem @ V2v1 @ A_27a )
=> ! [V3v2: $i] :
( ( mem @ V3v2 @ A_27a )
=> ! [V4v3: $i] :
( ( mem @ V4v3 @ A_27a )
=> ! [V5v: $i] :
( ( mem @ V5v @ A_27a )
=> ( ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eieee_2Eccode__CASE @ A_27a ) @ ( inj__ty_2Eieee_2Eccode @ V0x ) ) @ V1v0 ) @ V2v1 ) @ V3v2 ) @ V4v3 )
= V5v )
<=> ( ( ( V0x = fo__c_2Eieee_2EGt )
& ( V1v0 = V5v ) )
| ( ( V0x = fo__c_2Eieee_2ELt )
& ( V2v1 = V5v ) )
| ( ( V0x = fo__c_2Eieee_2EEq )
& ( V3v2 = V5v ) )
| ( ( V0x = fo__c_2Eieee_2EUn )
& ( V4v3 = V5v ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efcompare,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,V2b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__ty_2Eieee_2Eccode @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efcompare @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
= ( surj__ty_2Eieee_2Eccode @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eieee_2Eccode ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 ) ) ) @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ ( 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 @ V2b ) ) ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EUn ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eieee_2Eccode ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V1a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eieee_2Eccode ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2b ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2b ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EEq ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2ELt ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eieee_2Eccode ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V1a ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eieee_2Eccode ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2b ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2b ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EEq ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EGt ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eieee_2Eccode ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2b ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2b ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EGt ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eieee_2Eccode ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ ( 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 @ V2b ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 @ V2b ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2ELt ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eieee_2Eccode ) @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( 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 ) ) ) @ ( 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 @ V2b ) ) ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2ELt ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eieee_2Eccode ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ 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 ) ) ) @ ( 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 @ V2b ) ) ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EEq ) ) @ ( inj__ty_2Eieee_2Eccode @ fo__c_2Eieee_2EGt ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Eflt,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,V2b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eflt @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
<=> ( ( surj__ty_2Eieee_2Eccode @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efcompare @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
= fo__c_2Eieee_2ELt ) ) ).
thf(ax_thm_2Eieee_2Efle,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,V2b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efle @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
<=> ( ( ( surj__ty_2Eieee_2Eccode @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efcompare @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
= fo__c_2Eieee_2ELt )
| ( ( surj__ty_2Eieee_2Eccode @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efcompare @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
= fo__c_2Eieee_2EEq ) ) ) ).
thf(ax_thm_2Eieee_2Efgt,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,V2b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efgt @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
<=> ( ( surj__ty_2Eieee_2Eccode @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efcompare @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
= fo__c_2Eieee_2EGt ) ) ).
thf(ax_thm_2Eieee_2Efge,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,V2b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efge @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
<=> ( ( ( surj__ty_2Eieee_2Eccode @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efcompare @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
= fo__c_2Eieee_2EGt )
| ( ( surj__ty_2Eieee_2Eccode @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efcompare @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
= fo__c_2Eieee_2EEq ) ) ) ).
thf(ax_thm_2Eieee_2Efeq,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,V2b: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efeq @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
<=> ( ( surj__ty_2Eieee_2Eccode @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efcompare @ ( 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 ) ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V2b ) ) )
= fo__c_2Eieee_2EEq ) ) ).
thf(ax_thm_2Eieee_2Efloat__format,axiom,
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ c_2Eieee_2Efloat__format )
= ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__TY__DEF,axiom,
? [V0rep: $i] :
( ( mem @ V0rep @ ( arr @ ty_2Eieee_2Efloat @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Eieee_2Efloat ) @ ( ap @ c_2Eieee_2Eis__valid @ c_2Eieee_2Efloat__format ) ) @ V0rep ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__tybij,axiom,
( ! [V0a: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) )
= V0a )
& ! [V1r: 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 @ c_2Eieee_2Efloat__format ) @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1r ) ) )
<=> ( ( 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 @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V1r ) ) ) )
= V1r ) ) ) ).
thf(ax_thm_2Eieee_2EVal,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EVal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Eieee_2Evalof @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EFloat,axiom,
! [V0x: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2EFloat @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
= ( surj__ty_2Eieee_2Efloat @ ( 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 ) ) ) ) ) ).
thf(ax_thm_2Eieee_2ESign,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2ESign @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Esign @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EExponent,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2EExponent @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Eexponent @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EFraction,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2EFraction @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eieee_2Efraction @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EUlp,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Eieee_2EUlp @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( ap @ c_2Eieee_2Eulp @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EIsnan,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EIsnan @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__nan @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EInfinity,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EInfinity @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__infinity @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EIsnormal,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EIsnormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__normal @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EIsdenormal,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EIsdenormal @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__denormal @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EIszero,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EIszero @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__zero @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EFinite,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EFinite @ ( 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(ax_thm_2Eieee_2EIsintegral,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ c_2Eieee_2EIsintegral @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eieee_2Eis__integral @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EPlus__zero,axiom,
( fo__c_2Eieee_2EPlus__zero
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Eplus__zero @ c_2Eieee_2Efloat__format ) ) ) ) ).
thf(ax_thm_2Eieee_2EMinus__zero,axiom,
( fo__c_2Eieee_2EMinus__zero
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Eminus__zero @ c_2Eieee_2Efloat__format ) ) ) ) ).
thf(ax_thm_2Eieee_2EMinus__infinity,axiom,
( fo__c_2Eieee_2EMinus__infinity
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Eminus__infinity @ c_2Eieee_2Efloat__format ) ) ) ) ).
thf(ax_thm_2Eieee_2EPlus__infinity,axiom,
( fo__c_2Eieee_2EPlus__infinity
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Eplus__infinity @ c_2Eieee_2Efloat__format ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__add,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ ( ap @ c_2Eieee_2Efloat__add @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efadd @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__sub,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ ( ap @ c_2Eieee_2Efloat__sub @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efsub @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__mul,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ ( ap @ c_2Eieee_2Efloat__mul @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efmul @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__div,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ ( ap @ c_2Eieee_2Efloat__div @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efdiv @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__rem,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ ( ap @ c_2Eieee_2Efloat__rem @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efrem @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__sqrt,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat__sqrt @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efsqrt @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2EROUNDFLOAT,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2EROUNDFLOAT @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efintrnd @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__lt,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__lt @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Eflt @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__le,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__le @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efle @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__gt,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__gt @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efgt @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__ge,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__ge @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efge @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__eq,axiom,
! [V0a: tp__ty_2Eieee_2Efloat,V1b: tp__ty_2Eieee_2Efloat] :
( ( p @ ( ap @ ( ap @ c_2Eieee_2Efloat__eq @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efeq @ c_2Eieee_2Efloat__format ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V1b ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__neg,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat__neg @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ c_2Eieee_2Efneg @ c_2Eieee_2Efloat__format ) @ ( inj__ty_2Eieee_2Eroundmode @ fo__c_2Eieee_2ETo__nearest ) ) @ ( ap @ c_2Eieee_2Edefloat @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ) ).
thf(ax_thm_2Eieee_2Efloat__abs,axiom,
! [V0a: tp__ty_2Eieee_2Efloat] :
( ( surj__ty_2Eieee_2Efloat @ ( ap @ c_2Eieee_2Efloat__abs @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) )
= ( surj__ty_2Eieee_2Efloat @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eieee_2Efloat ) @ ( ap @ ( ap @ c_2Eieee_2Efloat__ge @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( inj__ty_2Eieee_2Efloat @ fo__c_2Eieee_2EPlus__zero ) ) ) @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) @ ( ap @ c_2Eieee_2Efloat__neg @ ( inj__ty_2Eieee_2Efloat @ V0a ) ) ) ) ) ).
%------------------------------------------------------------------------------