ITP001 Axioms: ITP139_7.ax
%------------------------------------------------------------------------------
% File : ITP139_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : float.ax [Gau19]
% : HL4139_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 334 ( 91 unt; 177 typ; 0 def)
% Number of atoms : 321 ( 126 equ)
% Maximal formula atoms : 20 ( 0 avg)
% Number of connectives : 194 ( 30 ~; 10 |; 90 &)
% ( 20 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 130 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 127 ( 81 >; 46 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 171 ( 171 usr; 75 con; 0-5 aty)
% Number of variables : 328 ( 277 !; 10 ?; 328 :)
% ( 41 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Eieee_2Efloat,type,
tyop_2Eieee_2Efloat: $tType ).
tff(tyop_2Eieee_2Eroundmode,type,
tyop_2Eieee_2Eroundmode: $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ereal_2E_2F_2E0,type,
c_2Ereal_2E_2F_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2E_2F_2E2,type,
c_2Ereal_2E_2F_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EEXP_2E0,type,
c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EEXP_2E2,type,
c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2EFST_2E0,type,
c_2Epair_2EFST_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).
tff(c_2Epair_2EFST_2E1,type,
c_2Epair_2EFST_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27a ) ).
tff(c_2Eieee_2EFinite_2E0,type,
c_2Eieee_2EFinite_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2EFinite_2E1,type,
c_2Eieee_2EFinite_2E1: tyop_2Eieee_2Efloat > tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eieee_2EInfinity_2E0,type,
c_2Eieee_2EInfinity_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2EInfinity_2E1,type,
c_2Eieee_2EInfinity_2E1: tyop_2Eieee_2Efloat > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2EIsdenormal_2E0,type,
c_2Eieee_2EIsdenormal_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2EIsdenormal_2E1,type,
c_2Eieee_2EIsdenormal_2E1: tyop_2Eieee_2Efloat > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2EIsnan_2E0,type,
c_2Eieee_2EIsnan_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2EIsnan_2E1,type,
c_2Eieee_2EIsnan_2E1: tyop_2Eieee_2Efloat > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2EIsnormal_2E0,type,
c_2Eieee_2EIsnormal_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2EIsnormal_2E1,type,
c_2Eieee_2EIsnormal_2E1: tyop_2Eieee_2Efloat > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2EIszero_2E0,type,
c_2Eieee_2EIszero_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2EIszero_2E1,type,
c_2Eieee_2EIszero_2E1: tyop_2Eieee_2Efloat > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2EMinus__infinity_2E0,type,
c_2Eieee_2EMinus__infinity_2E0: tyop_2Eieee_2Efloat ).
tff(c_2Eieee_2EMinus__zero_2E0,type,
c_2Eieee_2EMinus__zero_2E0: tyop_2Eieee_2Efloat ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eieee_2EPlus__infinity_2E0,type,
c_2Eieee_2EPlus__infinity_2E0: tyop_2Eieee_2Efloat ).
tff(c_2Eieee_2EPlus__zero_2E0,type,
c_2Eieee_2EPlus__zero_2E0: tyop_2Eieee_2Efloat ).
tff(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).
tff(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).
tff(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Eieee_2ETo__nearest_2E0,type,
c_2Eieee_2ETo__nearest_2E0: tyop_2Eieee_2Eroundmode ).
tff(c_2Eieee_2EVal_2E0,type,
c_2Eieee_2EVal_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Erealax_2Ereal) ).
tff(c_2Eieee_2EVal_2E1,type,
c_2Eieee_2EVal_2E1: tyop_2Eieee_2Efloat > tyop_2Erealax_2Ereal ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Eabs_2E0,type,
c_2Ereal_2Eabs_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Ereal_2Eabs_2E1,type,
c_2Ereal_2Eabs_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Eieee_2Ebias_2E0,type,
c_2Eieee_2Ebias_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Ebias_2E1,type,
c_2Eieee_2Ebias_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum ).
tff(c_2Eieee_2Ebottomfloat_2E0,type,
c_2Eieee_2Ebottomfloat_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Eieee_2Ebottomfloat_2E1,type,
c_2Eieee_2Ebottomfloat_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Eclosest_2E0,type,
c_2Eieee_2Eclosest_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a)))) ).
tff(c_2Eieee_2Eclosest_2E4,type,
c_2Eieee_2Eclosest_2E4:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Erealax_2Ereal ) > A_27a ) ).
tff(c_2Eieee_2Edefloat_2E0,type,
c_2Eieee_2Edefloat_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Eieee_2Edefloat_2E1,type,
c_2Eieee_2Edefloat_2E1: tyop_2Eieee_2Efloat > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Eemax_2E0,type,
c_2Eieee_2Eemax_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Eemax_2E1,type,
c_2Eieee_2Eemax_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum ).
tff(c_2Efloat_2Eerror_2E0,type,
c_2Efloat_2Eerror_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Efloat_2Eerror_2E1,type,
c_2Efloat_2Eerror_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Eieee_2Eexponent_2E0,type,
c_2Eieee_2Eexponent_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Eexponent_2E1,type,
c_2Eieee_2Eexponent_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) > tyop_2Enum_2Enum ).
tff(c_2Eieee_2Eexpwidth_2E0,type,
c_2Eieee_2Eexpwidth_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Eexpwidth_2E1,type,
c_2Eieee_2Eexpwidth_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum ).
tff(c_2Eieee_2Efloat_2E0,type,
c_2Eieee_2Efloat_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Eieee_2Efloat) ).
tff(c_2Eieee_2Efloat_2E1,type,
c_2Eieee_2Efloat_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) > tyop_2Eieee_2Efloat ).
tff(c_2Eieee_2Efloat__add_2E0,type,
c_2Eieee_2Efloat__add_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat)) ).
tff(c_2Eieee_2Efloat__add_2E2,type,
c_2Eieee_2Efloat__add_2E2: ( tyop_2Eieee_2Efloat * tyop_2Eieee_2Efloat ) > tyop_2Eieee_2Efloat ).
tff(c_2Eieee_2Efloat__div_2E0,type,
c_2Eieee_2Efloat__div_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat)) ).
tff(c_2Eieee_2Efloat__div_2E2,type,
c_2Eieee_2Efloat__div_2E2: ( tyop_2Eieee_2Efloat * tyop_2Eieee_2Efloat ) > tyop_2Eieee_2Efloat ).
tff(c_2Eieee_2Efloat__eq_2E0,type,
c_2Eieee_2Efloat__eq_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool)) ).
tff(c_2Eieee_2Efloat__eq_2E2,type,
c_2Eieee_2Efloat__eq_2E2: ( tyop_2Eieee_2Efloat * tyop_2Eieee_2Efloat ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Efloat__format_2E0,type,
c_2Eieee_2Efloat__format_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Efloat__ge_2E0,type,
c_2Eieee_2Efloat__ge_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool)) ).
tff(c_2Eieee_2Efloat__ge_2E2,type,
c_2Eieee_2Efloat__ge_2E2: ( tyop_2Eieee_2Efloat * tyop_2Eieee_2Efloat ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Efloat__gt_2E0,type,
c_2Eieee_2Efloat__gt_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool)) ).
tff(c_2Eieee_2Efloat__gt_2E2,type,
c_2Eieee_2Efloat__gt_2E2: ( tyop_2Eieee_2Efloat * tyop_2Eieee_2Efloat ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Efloat__le_2E0,type,
c_2Eieee_2Efloat__le_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool)) ).
tff(c_2Eieee_2Efloat__le_2E2,type,
c_2Eieee_2Efloat__le_2E2: ( tyop_2Eieee_2Efloat * tyop_2Eieee_2Efloat ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Efloat__lt_2E0,type,
c_2Eieee_2Efloat__lt_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool)) ).
tff(c_2Eieee_2Efloat__lt_2E2,type,
c_2Eieee_2Efloat__lt_2E2: ( tyop_2Eieee_2Efloat * tyop_2Eieee_2Efloat ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Efloat__mul_2E0,type,
c_2Eieee_2Efloat__mul_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat)) ).
tff(c_2Eieee_2Efloat__mul_2E2,type,
c_2Eieee_2Efloat__mul_2E2: ( tyop_2Eieee_2Efloat * tyop_2Eieee_2Efloat ) > tyop_2Eieee_2Efloat ).
tff(c_2Eieee_2Efloat__sub_2E0,type,
c_2Eieee_2Efloat__sub_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat)) ).
tff(c_2Eieee_2Efloat__sub_2E2,type,
c_2Eieee_2Efloat__sub_2E2: ( tyop_2Eieee_2Efloat * tyop_2Eieee_2Efloat ) > tyop_2Eieee_2Efloat ).
tff(c_2Eieee_2Efraction_2E0,type,
c_2Eieee_2Efraction_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Efraction_2E1,type,
c_2Eieee_2Efraction_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) > tyop_2Enum_2Enum ).
tff(c_2Eieee_2Efracwidth_2E0,type,
c_2Eieee_2Efracwidth_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Efracwidth_2E1,type,
c_2Eieee_2Efracwidth_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum ).
tff(c_2Erealax_2Einv_2E0,type,
c_2Erealax_2Einv_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Erealax_2Einv_2E1,type,
c_2Erealax_2Einv_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Eieee_2Eis__closest_2E0,type,
c_2Eieee_2Eis__closest_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Eieee_2Eis__closest_2E4,type,
c_2Eieee_2Eis__closest_2E4:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Erealax_2Ereal * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eieee_2Eis__finite_2E0,type,
c_2Eieee_2Eis__finite_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)) ).
tff(c_2Eieee_2Eis__finite_2E2,type,
c_2Eieee_2Eis__finite_2E2: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Eis__valid_2E0,type,
c_2Eieee_2Eis__valid_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)) ).
tff(c_2Eieee_2Eis__valid_2E2,type,
c_2Eieee_2Eis__valid_2E2: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Elargest_2E0,type,
c_2Eieee_2Elargest_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Erealax_2Ereal) ).
tff(c_2Eieee_2Elargest_2E1,type,
c_2Eieee_2Elargest_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Erealax_2Ereal ).
tff(c_2Eieee_2Eminus__infinity_2E0,type,
c_2Eieee_2Eminus__infinity_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Eieee_2Eminus__infinity_2E1,type,
c_2Eieee_2Eminus__infinity_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Eminus__zero_2E0,type,
c_2Eieee_2Eminus__zero_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Eieee_2Eminus__zero_2E1,type,
c_2Eieee_2Eminus__zero_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Efloat_2Enormalizes_2E0,type,
c_2Efloat_2Enormalizes_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool) ).
tff(c_2Efloat_2Enormalizes_2E1,type,
c_2Efloat_2Enormalizes_2E1: tyop_2Erealax_2Ereal > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Eplus__infinity_2E0,type,
c_2Eieee_2Eplus__infinity_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Eieee_2Eplus__infinity_2E1,type,
c_2Eieee_2Eplus__infinity_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Eplus__zero_2E0,type,
c_2Eieee_2Eplus__zero_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Eieee_2Eplus__zero_2E1,type,
c_2Eieee_2Eplus__zero_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Ereal_2Epow_2E0,type,
c_2Ereal_2Epow_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2Epow_2E2,type,
c_2Ereal_2Epow_2E2: ( tyop_2Erealax_2Ereal * tyop_2Enum_2Enum ) > tyop_2Erealax_2Ereal ).
tff(c_2Erealax_2Ereal__add_2E0,type,
c_2Erealax_2Ereal__add_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Erealax_2Ereal__add_2E2,type,
c_2Erealax_2Ereal__add_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__ge_2E0,type,
c_2Ereal_2Ereal__ge_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__ge_2E2,type,
c_2Ereal_2Ereal__ge_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Ereal__gt_2E0,type,
c_2Ereal_2Ereal__gt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__gt_2E2,type,
c_2Ereal_2Ereal__gt_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Erealax_2Ereal__lt_2E0,type,
c_2Erealax_2Ereal__lt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Erealax_2Ereal__lt_2E2,type,
c_2Erealax_2Ereal__lt_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Ereal__lte_2E0,type,
c_2Ereal_2Ereal__lte_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__lte_2E2,type,
c_2Ereal_2Ereal__lte_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Erealax_2Ereal__mul_2E0,type,
c_2Erealax_2Ereal__mul_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Erealax_2Ereal__mul_2E2,type,
c_2Erealax_2Ereal__mul_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Erealax_2Ereal__neg_2E0,type,
c_2Erealax_2Ereal__neg_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Erealax_2Ereal__neg_2E1,type,
c_2Erealax_2Ereal__neg_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__of__num_2E0,type,
c_2Ereal_2Ereal__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) ).
tff(c_2Ereal_2Ereal__of__num_2E1,type,
c_2Ereal_2Ereal__of__num_2E1: tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__sub_2E0,type,
c_2Ereal_2Ereal__sub_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2Ereal__sub_2E2,type,
c_2Ereal_2Ereal__sub_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Eieee_2Eround_2E0,type,
c_2Eieee_2Eround_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))) ).
tff(c_2Eieee_2Eround_2E3,type,
c_2Eieee_2Eround_2E3: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Eieee_2Eroundmode * tyop_2Erealax_2Ereal ) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Esign_2E0,type,
c_2Eieee_2Esign_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Esign_2E1,type,
c_2Eieee_2Esign_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) > tyop_2Enum_2Enum ).
tff(c_2Eieee_2Ethreshold_2E0,type,
c_2Eieee_2Ethreshold_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Erealax_2Ereal) ).
tff(c_2Eieee_2Ethreshold_2E1,type,
c_2Eieee_2Ethreshold_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Erealax_2Ereal ).
tff(c_2Eieee_2Etopfloat_2E0,type,
c_2Eieee_2Etopfloat_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Eieee_2Etopfloat_2E1,type,
c_2Eieee_2Etopfloat_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Evalof_2E0,type,
c_2Eieee_2Evalof_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal)) ).
tff(c_2Eieee_2Evalof_2E2,type,
c_2Eieee_2Evalof_2E2: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ) > tyop_2Erealax_2Ereal ).
tff(c_2Eieee_2Ezerosign_2E0,type,
c_2Eieee_2Ezerosign_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))) ).
tff(c_2Eieee_2Ezerosign_2E3,type,
c_2Eieee_2Ezerosign_2E3: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Enum_2Enum * tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2E_2F_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2E_2F_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2E_2F_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Erealax_2Ereal,X2_2E0: tyop_2Erealax_2Ereal] : ( c_2Ebool_2ECOND_2E3(tyop_2Erealax_2Ereal,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Ebool_2ECOND_2E0(tyop_2Erealax_2Ereal),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epair_2EFST_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Epair_2EFST_2E1(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum,c_2Epair_2EFST_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2EFinite_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EFinite_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2EInfinity_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EInfinity_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2EIsdenormal_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EIsdenormal_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,c_2Eieee_2EIsdenormal_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2EIsnan_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EIsnan_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2EIsnormal_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EIsnormal_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,c_2Eieee_2EIsnormal_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2EIszero_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EIszero_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2ESND_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2ESND_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2EVal_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EVal_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ereal_2Eabs_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Eabs_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Ebias_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Ebias_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Eieee_2Ebias_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Ebottomfloat_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Ebottomfloat_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Ebottomfloat_2E0,X0_2E0) ) ).
tff(arityeq4_2Ec_2Eieee_2Eclosest_2E4_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X3_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),c_2Eieee_2Eclosest_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Edefloat_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Edefloat_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Edefloat_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eemax_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eemax_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Eieee_2Eemax_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Efloat_2Eerror_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Efloat_2Eerror_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Efloat_2Eerror_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eexponent_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Eexponent_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eexpwidth_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eexpwidth_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Eieee_2Eexpwidth_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Efloat_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efloat_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Eieee_2Efloat,c_2Eieee_2Efloat_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Efloat__add_2E2,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat,X1_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat,app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat),c_2Eieee_2Efloat__add_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Efloat__div_2E2,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat,X1_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__div_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat,app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat),c_2Eieee_2Efloat__div_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Efloat__eq_2E2,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat,X1_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__eq_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2Efloat__eq_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Efloat__ge_2E2,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat,X1_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__ge_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2Efloat__ge_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Efloat__gt_2E2,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat,X1_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__gt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2Efloat__gt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Efloat__le_2E2,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat,X1_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__le_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2Efloat__le_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Efloat__lt_2E2,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat,X1_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2Efloat__lt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Efloat__mul_2E2,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat,X1_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat,app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat),c_2Eieee_2Efloat__mul_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Efloat__sub_2E2,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat,X1_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__sub_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat,app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat),c_2Eieee_2Efloat__sub_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Efraction_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efraction_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum,c_2Eieee_2Efraction_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Efracwidth_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Efracwidth_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Eieee_2Efracwidth_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Erealax_2Einv_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Einv_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Einv_2E0,X0_2E0) ) ).
tff(arityeq4_2Ec_2Eieee_2Eis__closest_2E4_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X2_2E0: tyop_2Erealax_2Ereal,X3_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Eis__closest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),c_2Eieee_2Eis__closest_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Eis__finite_2E2,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Eis__finite_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Eieee_2Eis__finite_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Eis__valid_2E2,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Eis__valid_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Eieee_2Eis__valid_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Elargest_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Elargest_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Erealax_2Ereal,c_2Eieee_2Elargest_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eminus__infinity_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eminus__infinity_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eminus__infinity_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eminus__zero_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eminus__zero_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eminus__zero_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Efloat_2Enormalizes_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Efloat_2Enormalizes_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,c_2Efloat_2Enormalizes_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eplus__infinity_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eplus__infinity_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eplus__infinity_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eplus__zero_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eplus__zero_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eplus__zero_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Epow_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Epow_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),c_2Ereal_2Epow_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__add_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__ge_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__ge_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__ge_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__gt_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__gt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__gt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Erealax_2Ereal__lt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__lte_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__mul_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erealax_2Ereal__neg_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__neg_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Ereal__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__sub_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__sub_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2Ereal__sub_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Eround_2E3,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eieee_2Eroundmode,X2_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eround_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Eieee_2Eround_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Esign_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Esign_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum,c_2Eieee_2Esign_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Ethreshold_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Ethreshold_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Etopfloat_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Etopfloat_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Etopfloat_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Evalof_2E2,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Evalof_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),c_2Eieee_2Evalof_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Ezerosign_2E3,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Ezerosign_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Eieee_2Ezerosign_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Efloat_2Eerror__def,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Efloat_2Eerror_2E1(V0x_2E0) = c_2Ereal_2Ereal__sub_2E2(c_2Eieee_2EVal_2E1(c_2Eieee_2Efloat_2E1(c_2Eieee_2Eround_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,V0x_2E0))),V0x_2E0) ) ).
tff(thm_2Efloat_2Enormalizes__def,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Efloat_2Enormalizes_2E1(V0x_2E0))
<=> ( p(c_2Ereal_2Ereal__lte_2E2(c_2Erealax_2Einv_2E1(c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2D_2E2(c_2Eieee_2Ebias_2E1(c_2Eieee_2Efloat__format_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Ereal_2Eabs_2E1(V0x_2E0)))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(V0x_2E0),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0))) ) ) ).
tff(thm_2Efloat_2ESIGN,axiom,
! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Esign_2E1(V0a_2E0) = c_2Epair_2EFST_2E1(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0a_2E0) ) ).
tff(thm_2Efloat_2EEXPONENT,axiom,
! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Eexponent_2E1(V0a_2E0) = c_2Epair_2EFST_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0a_2E0)) ) ).
tff(thm_2Efloat_2EFRACTION,axiom,
! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efraction_2E1(V0a_2E0) = c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0a_2E0)) ) ).
tff(thm_2Efloat_2EIS__VALID,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,V1a_2E0))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Esign_2E1(V1a_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Eexponent_2E1(V1a_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eieee_2Eexpwidth_2E1(V0X_2E0))))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Efraction_2E1(V1a_2E0),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eieee_2Efracwidth_2E1(V0X_2E0)))) ) ) ).
tff(thm_2Efloat_2EVALOF,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)] :
( ! [V1a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( p(app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,F0_2E0,V1a_2E0))
<=> ( c_2Eieee_2Eexponent_2E1(V1a_2E0) = c_2Enum_2E0_2E0 ) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Evalof_2E2(V0X_2E0,V1a_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Erealax_2Ereal,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,F0_2E0,V1a_2E0),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Epow_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Eieee_2Esign_2E1(V1a_2E0)),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Eieee_2Ebias_2E1(V0X_2E0)))),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Eieee_2Efraction_2E1(V1a_2E0)),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Eieee_2Efracwidth_2E1(V0X_2E0)))),c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Epow_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Eieee_2Esign_2E1(V1a_2E0)),c_2Ereal_2E_2F_2E2(c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Eieee_2Eexponent_2E1(V1a_2E0)),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Eieee_2Ebias_2E1(V0X_2E0)))),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Eieee_2Efraction_2E1(V1a_2E0)),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Eieee_2Efracwidth_2E1(V0X_2E0)))))) ) ) ).
tff(thm_2Efloat_2EIS__VALID__DEFLOAT,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : p(c_2Eieee_2Eis__valid_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0))) ).
tff(thm_2Efloat_2EIS__FINITE__EXPLICIT,axiom,
! [V0a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( p(c_2Eieee_2Eis__finite_2E2(c_2Eieee_2Efloat__format_2E0,V0a_2E0))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Esign_2E1(V0a_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Eexponent_2E1(V0a_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))))))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Efraction_2E1(V0a_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))))))) ) ) ).
tff(thm_2Efloat_2EFLOAT__CASES,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] :
( p(c_2Eieee_2EIsnan_2E1(V0a_2E0))
| p(c_2Eieee_2EInfinity_2E1(V0a_2E0))
| p(c_2Eieee_2EIsnormal_2E1(V0a_2E0))
| p(c_2Eieee_2EIsdenormal_2E1(V0a_2E0))
| p(c_2Eieee_2EIszero_2E1(V0a_2E0)) ) ).
tff(thm_2Efloat_2EFLOAT__CASES__FINITE,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] :
( p(c_2Eieee_2EIsnan_2E1(V0a_2E0))
| p(c_2Eieee_2EInfinity_2E1(V0a_2E0))
| p(c_2Eieee_2EFinite_2E1(V0a_2E0)) ) ).
tff(thm_2Efloat_2EFLOAT__DISTINCT,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] :
( ~ ( p(c_2Eieee_2EIsnan_2E1(V0a_2E0))
& p(c_2Eieee_2EInfinity_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EIsnan_2E1(V0a_2E0))
& p(c_2Eieee_2EIsnormal_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EIsnan_2E1(V0a_2E0))
& p(c_2Eieee_2EIsdenormal_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EIsnan_2E1(V0a_2E0))
& p(c_2Eieee_2EIszero_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EInfinity_2E1(V0a_2E0))
& p(c_2Eieee_2EIsnormal_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EInfinity_2E1(V0a_2E0))
& p(c_2Eieee_2EIsdenormal_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EInfinity_2E1(V0a_2E0))
& p(c_2Eieee_2EIszero_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EIsnormal_2E1(V0a_2E0))
& p(c_2Eieee_2EIsdenormal_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EIsnormal_2E1(V0a_2E0))
& p(c_2Eieee_2EIszero_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EIsdenormal_2E1(V0a_2E0))
& p(c_2Eieee_2EIszero_2E1(V0a_2E0)) ) ) ).
tff(thm_2Efloat_2EFLOAT__DISTINCT__FINITE,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] :
( ~ ( p(c_2Eieee_2EIsnan_2E1(V0a_2E0))
& p(c_2Eieee_2EInfinity_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EIsnan_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V0a_2E0)) )
& ~ ( p(c_2Eieee_2EInfinity_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V0a_2E0)) ) ) ).
tff(thm_2Efloat_2EFLOAT__INFINITIES__SIGNED,axiom,
( ( c_2Eieee_2Esign_2E1(c_2Eieee_2Edefloat_2E1(c_2Eieee_2EPlus__infinity_2E0)) = c_2Enum_2E0_2E0 )
& ( c_2Eieee_2Esign_2E1(c_2Eieee_2Edefloat_2E1(c_2Eieee_2EMinus__infinity_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Efloat_2EINFINITY__IS__INFINITY,axiom,
( p(c_2Eieee_2EInfinity_2E1(c_2Eieee_2EPlus__infinity_2E0))
& p(c_2Eieee_2EInfinity_2E1(c_2Eieee_2EMinus__infinity_2E0)) ) ).
tff(thm_2Efloat_2EZERO__IS__ZERO,axiom,
( p(c_2Eieee_2EIszero_2E1(c_2Eieee_2EPlus__zero_2E0))
& p(c_2Eieee_2EIszero_2E1(c_2Eieee_2EMinus__zero_2E0)) ) ).
tff(thm_2Efloat_2EINFINITY__NOT__NAN,axiom,
( ~ p(c_2Eieee_2EIsnan_2E1(c_2Eieee_2EPlus__infinity_2E0))
& ~ p(c_2Eieee_2EIsnan_2E1(c_2Eieee_2EMinus__infinity_2E0)) ) ).
tff(thm_2Efloat_2EZERO__NOT__NAN,axiom,
( ~ p(c_2Eieee_2EIsnan_2E1(c_2Eieee_2EPlus__zero_2E0))
& ~ p(c_2Eieee_2EIsnan_2E1(c_2Eieee_2EMinus__zero_2E0)) ) ).
tff(thm_2Efloat_2EFLOAT__INFINITIES,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] :
( p(c_2Eieee_2EInfinity_2E1(V0a_2E0))
<=> ( p(c_2Eieee_2Efloat__eq_2E2(V0a_2E0,c_2Eieee_2EPlus__infinity_2E0))
| p(c_2Eieee_2Efloat__eq_2E2(V0a_2E0,c_2Eieee_2EMinus__infinity_2E0)) ) ) ).
tff(thm_2Efloat_2EFLOAT__INFINITES__DISTINCT,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] :
~ ( p(c_2Eieee_2Efloat__eq_2E2(V0a_2E0,c_2Eieee_2EPlus__infinity_2E0))
& p(c_2Eieee_2Efloat__eq_2E2(V0a_2E0,c_2Eieee_2EMinus__infinity_2E0)) ) ).
tff(thm_2Efloat_2EFLOAT__LT,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0)) )
=> ( c_2Eieee_2Efloat__lt_2E2(V0a_2E0,V1b_2E0) = c_2Erealax_2Ereal__lt_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)) ) ) ).
tff(thm_2Efloat_2EFLOAT__GT,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0)) )
=> ( c_2Eieee_2Efloat__gt_2E2(V0a_2E0,V1b_2E0) = c_2Ereal_2Ereal__gt_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)) ) ) ).
tff(thm_2Efloat_2EFLOAT__LE,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0)) )
=> ( c_2Eieee_2Efloat__le_2E2(V0a_2E0,V1b_2E0) = c_2Ereal_2Ereal__lte_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)) ) ) ).
tff(thm_2Efloat_2EFLOAT__GE,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0)) )
=> ( c_2Eieee_2Efloat__ge_2E2(V0a_2E0,V1b_2E0) = c_2Ereal_2Ereal__ge_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)) ) ) ).
tff(thm_2Efloat_2EFLOAT__EQ,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0)) )
=> ( p(c_2Eieee_2Efloat__eq_2E2(V0a_2E0,V1b_2E0))
<=> ( c_2Eieee_2EVal_2E1(V0a_2E0) = c_2Eieee_2EVal_2E1(V1b_2E0) ) ) ) ).
tff(thm_2Efloat_2EFLOAT__EQ__REFL,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] :
( p(c_2Eieee_2Efloat__eq_2E2(V0a_2E0,V0a_2E0))
<=> ~ p(c_2Eieee_2EIsnan_2E1(V0a_2E0)) ) ).
tff(thm_2Efloat_2EIS__VALID__SPECIAL,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,c_2Eieee_2Eminus__infinity_2E1(V0X_2E0)))
& p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,c_2Eieee_2Eplus__infinity_2E1(V0X_2E0)))
& p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,c_2Eieee_2Etopfloat_2E1(V0X_2E0)))
& p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,c_2Eieee_2Ebottomfloat_2E1(V0X_2E0)))
& p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,c_2Eieee_2Eplus__zero_2E1(V0X_2E0)))
& p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,c_2Eieee_2Eminus__zero_2E1(V0X_2E0))) ) ).
tff(thm_2Efloat_2EIS__CLOSEST__EXISTS,axiom,
! [V0v_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V1x_2E0: tyop_2Erealax_2Ereal,V2s_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V2s_2E0))
=> ( ( V2s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) )
=> ? [V3a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : p(c_2Eieee_2Eis__closest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0v_2E0,V2s_2E0,V1x_2E0,V3a_2E0)) ) ) ).
tff(thm_2Efloat_2ECLOSEST__IS__EVERYTHING,axiom,
! [V0v_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V1p_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V2s_2E0))
=> ( ( V2s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) )
=> ( p(c_2Eieee_2Eis__closest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0v_2E0,V2s_2E0,V3x_2E0,c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0v_2E0,V1p_2E0,V2s_2E0,V3x_2E0)))
& ( ? [V4b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( p(c_2Eieee_2Eis__closest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0v_2E0,V2s_2E0,V3x_2E0,V4b_2E0))
& p(app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V1p_2E0,V4b_2E0)) )
=> p(app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V1p_2E0,c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0v_2E0,V1p_2E0,V2s_2E0,V3x_2E0))) ) ) ) ) ).
tff(thm_2Efloat_2ECLOSEST__IN__SET,axiom,
! [V0v_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V1p_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2x_2E0: tyop_2Erealax_2Ereal,V3s_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3s_2E0))
=> ( ( V3s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) )
=> p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0v_2E0,V1p_2E0,V3s_2E0,V2x_2E0),V3s_2E0)) ) ) ).
tff(thm_2Efloat_2ECLOSEST__IS__CLOSEST,axiom,
! [V0v_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V1p_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2x_2E0: tyop_2Erealax_2Ereal,V3s_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3s_2E0))
=> ( ( V3s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) )
=> p(c_2Eieee_2Eis__closest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0v_2E0,V3s_2E0,V2x_2E0,c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0v_2E0,V1p_2E0,V3s_2E0,V2x_2E0))) ) ) ).
tff(thm_2Efloat_2EIS__VALID__FINITE,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))] :
( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V1a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V1a_2E0,c_2Eieee_2Eis__valid_2E2(V0X_2E0,V1a_2E0)) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0)))) ) ).
tff(thm_2Efloat_2EIS__FINITE__FINITE,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))] :
( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V1a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V1a_2E0,c_2Eieee_2Eis__finite_2E2(V0X_2E0,V1a_2E0)) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0)))) ) ).
tff(thm_2Efloat_2EIS__VALID__NONEMPTY,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))] :
( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V1a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V1a_2E0,c_2Eieee_2Eis__valid_2E2(V0X_2E0,V1a_2E0)) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0)) != c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ) ) ).
tff(thm_2Efloat_2EIS__FINITE__NONEMPTY,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))] :
( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V1a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V1a_2E0,c_2Eieee_2Eis__finite_2E2(V0X_2E0,V1a_2E0)) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0)) != c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ) ) ).
tff(thm_2Efloat_2EIS__FINITE__CLOSEST,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))] :
( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V4a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V4a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V4a_2E0,c_2Eieee_2Eis__finite_2E2(V0X_2E0,V4a_2E0)) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1v_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V2p_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3x_2E0: tyop_2Erealax_2Ereal] : p(c_2Eieee_2Eis__finite_2E2(V0X_2E0,c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1v_2E0,V2p_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0)),V3x_2E0))) ) ).
tff(thm_2Efloat_2EIS__VALID__CLOSEST,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))] :
( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V4a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V4a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V4a_2E0,c_2Eieee_2Eis__finite_2E2(V0X_2E0,V4a_2E0)) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1v_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V2p_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3x_2E0: tyop_2Erealax_2Ereal] : p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1v_2E0,V2p_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0)),V3x_2E0))) ) ).
tff(thm_2Efloat_2EIS__VALID__ROUND,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1x_2E0: tyop_2Erealax_2Ereal] : p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,c_2Eieee_2Eround_2E3(V0X_2E0,c_2Eieee_2ETo__nearest_2E0,V1x_2E0))) ).
tff(thm_2Efloat_2EDEFLOAT__FLOAT__ROUND,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Edefloat_2E1(c_2Eieee_2Efloat_2E1(c_2Eieee_2Eround_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,V0x_2E0))) = c_2Eieee_2Eround_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,V0x_2E0) ) ).
tff(thm_2Efloat_2EDEFLOAT__FLOAT__ZEROSIGN__ROUND,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1b_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Edefloat_2E1(c_2Eieee_2Efloat_2E1(c_2Eieee_2Ezerosign_2E3(c_2Eieee_2Efloat__format_2E0,V1b_2E0,c_2Eieee_2Eround_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,V0x_2E0)))) = c_2Eieee_2Ezerosign_2E3(c_2Eieee_2Efloat__format_2E0,V1b_2E0,c_2Eieee_2Eround_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,V0x_2E0)) ) ).
tff(thm_2Efloat_2EVALOF__DEFLOAT__FLOAT__ZEROSIGN__ROUND,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1b_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Evalof_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(c_2Eieee_2Efloat_2E1(c_2Eieee_2Ezerosign_2E3(c_2Eieee_2Efloat__format_2E0,V1b_2E0,c_2Eieee_2Eround_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,V0x_2E0))))) = c_2Eieee_2Evalof_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Eround_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,V0x_2E0)) ) ).
tff(thm_2Efloat_2EISFINITE,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EFinite_2E1(V0a_2E0) = c_2Eieee_2Eis__finite_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Efloat_2EVAL__FINITE,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] :
( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(c_2Eieee_2EVal_2E1(V0a_2E0)),c_2Eieee_2Elargest_2E1(c_2Eieee_2Efloat__format_2E0))) ) ).
tff(thm_2Efloat_2EFLOAT__THRESHOLD__EXPLICIT,axiom,
c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ).
tff(thm_2Efloat_2EFLOAT__LARGEST__EXPLICIT,axiom,
c_2Eieee_2Elargest_2E1(c_2Eieee_2Efloat__format_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ).
tff(thm_2Efloat_2EVAL__THRESHOLD,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] :
( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
=> p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Eieee_2EVal_2E1(V0a_2E0)),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0))) ) ).
tff(thm_2Efloat_2EERROR__IS__ZERO,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1x_2E0: tyop_2Erealax_2Ereal] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& ( c_2Eieee_2EVal_2E1(V0a_2E0) = V1x_2E0 ) )
=> ( c_2Efloat_2Eerror_2E1(V1x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ).
tff(thm_2Efloat_2EERROR__BOUND__NORM__STRONG,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal,V1j_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(V0x_2E0),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0)))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(V0x_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Enum_2ESUC_2E1(V1j_2E0)),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))))) )
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(c_2Efloat_2Eerror_2E1(V0x_2E0)),c_2Ereal_2E_2F_2E2(c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V1j_2E0),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))))))) ) ).
tff(thm_2Efloat_2EREAL__IN__BINADE,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Efloat_2Enormalizes_2E1(V0x_2E0))
=> ? [V1j_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1j_2E0,c_2Earithmetic_2E_2D_2E2(c_2Eieee_2Eemax_2E1(c_2Eieee_2Efloat__format_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))
& p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2E_2F_2E2(c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V1j_2E0),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Ereal_2Eabs_2E1(V0x_2E0)))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(V0x_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Enum_2ESUC_2E1(V1j_2E0)),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))))))) ) ) ).
tff(thm_2Efloat_2EERROR__BOUND__NORM__STRONG__NORMALIZE,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Efloat_2Enormalizes_2E1(V0x_2E0))
=> ? [V1j_2E0: tyop_2Enum_2Enum] : p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(c_2Efloat_2Eerror_2E1(V0x_2E0)),c_2Ereal_2E_2F_2E2(c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V1j_2E0),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))))))) ) ).
tff(thm_2Efloat_2ERELATIVE__ERROR,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Efloat_2Enormalizes_2E1(V0x_2E0))
=> ? [V1e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V1e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
& ( c_2Eieee_2EVal_2E1(c_2Eieee_2Efloat_2E1(c_2Eieee_2Eround_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,V0x_2E0))) = c_2Erealax_2Ereal__mul_2E2(V0x_2E0,c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1e_2E0)) ) ) ) ).
tff(thm_2Efloat_2EDEFLOAT__FLOAT__ZEROSIGN__ROUND__FINITE,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(V1x_2E0),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0)))
=> p(c_2Eieee_2Eis__finite_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(c_2Eieee_2Efloat_2E1(c_2Eieee_2Ezerosign_2E3(c_2Eieee_2Efloat__format_2E0,V0b_2E0,c_2Eieee_2Eround_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,V1x_2E0)))))) ) ).
tff(thm_2Efloat_2EFLOAT__ADD,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Erealax_2Ereal__add_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0))),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0))) )
=> ( p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__add_2E2(V0a_2E0,V1b_2E0)))
& ( c_2Eieee_2EVal_2E1(c_2Eieee_2Efloat__add_2E2(V0a_2E0,V1b_2E0)) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__add_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)),c_2Efloat_2Eerror_2E1(c_2Erealax_2Ereal__add_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)))) ) ) ) ).
tff(thm_2Efloat_2EFLOAT__SUB,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Ereal_2Ereal__sub_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0))),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0))) )
=> ( p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__sub_2E2(V0a_2E0,V1b_2E0)))
& ( c_2Eieee_2EVal_2E1(c_2Eieee_2Efloat__sub_2E2(V0a_2E0,V1b_2E0)) = c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__sub_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)),c_2Efloat_2Eerror_2E1(c_2Ereal_2Ereal__sub_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)))) ) ) ) ).
tff(thm_2Efloat_2EFLOAT__MUL,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Erealax_2Ereal__mul_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0))),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0))) )
=> ( p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__mul_2E2(V0a_2E0,V1b_2E0)))
& ( c_2Eieee_2EVal_2E1(c_2Eieee_2Efloat__mul_2E2(V0a_2E0,V1b_2E0)) = c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)),c_2Efloat_2Eerror_2E1(c_2Erealax_2Ereal__mul_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)))) ) ) ) ).
tff(thm_2Efloat_2EFLOAT__DIV,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0))
& ~ p(c_2Eieee_2EIszero_2E1(V1b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Ereal_2E_2F_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0))),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0))) )
=> ( p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__div_2E2(V0a_2E0,V1b_2E0)))
& ( c_2Eieee_2EVal_2E1(c_2Eieee_2Efloat__div_2E2(V0a_2E0,V1b_2E0)) = c_2Erealax_2Ereal__add_2E2(c_2Ereal_2E_2F_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)),c_2Efloat_2Eerror_2E1(c_2Ereal_2E_2F_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)))) ) ) ) ).
tff(thm_2Efloat_2EFLOAT__ADD__FINITE,axiom,
! [V0b_2E0: tyop_2Eieee_2Efloat,V1a_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V1a_2E0))
& p(c_2Eieee_2EFinite_2E1(V0b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Erealax_2Ereal__add_2E2(c_2Eieee_2EVal_2E1(V1a_2E0),c_2Eieee_2EVal_2E1(V0b_2E0))),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0))) )
=> p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__add_2E2(V1a_2E0,V0b_2E0))) ) ).
tff(thm_2Efloat_2EFLOAT__SUB__FINITE,axiom,
! [V0b_2E0: tyop_2Eieee_2Efloat,V1a_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V1a_2E0))
& p(c_2Eieee_2EFinite_2E1(V0b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Ereal_2Ereal__sub_2E2(c_2Eieee_2EVal_2E1(V1a_2E0),c_2Eieee_2EVal_2E1(V0b_2E0))),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0))) )
=> p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__sub_2E2(V1a_2E0,V0b_2E0))) ) ).
tff(thm_2Efloat_2EFLOAT__MUL__FINITE,axiom,
! [V0b_2E0: tyop_2Eieee_2Efloat,V1a_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V1a_2E0))
& p(c_2Eieee_2EFinite_2E1(V0b_2E0))
& p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Eabs_2E1(c_2Erealax_2Ereal__mul_2E2(c_2Eieee_2EVal_2E1(V1a_2E0),c_2Eieee_2EVal_2E1(V0b_2E0))),c_2Eieee_2Ethreshold_2E1(c_2Eieee_2Efloat__format_2E0))) )
=> p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__mul_2E2(V1a_2E0,V0b_2E0))) ) ).
tff(thm_2Efloat_2EFLOAT__ADD__RELATIVE,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0))
& p(c_2Efloat_2Enormalizes_2E1(c_2Erealax_2Ereal__add_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)))) )
=> ( p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__add_2E2(V0a_2E0,V1b_2E0)))
& ? [V2e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V2e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
& ( c_2Eieee_2EVal_2E1(c_2Eieee_2Efloat__add_2E2(V0a_2E0,V1b_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__add_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).
tff(thm_2Efloat_2EFLOAT__SUB__RELATIVE,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0))
& p(c_2Efloat_2Enormalizes_2E1(c_2Ereal_2Ereal__sub_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)))) )
=> ( p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__sub_2E2(V0a_2E0,V1b_2E0)))
& ? [V2e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V2e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
& ( c_2Eieee_2EVal_2E1(c_2Eieee_2Efloat__sub_2E2(V0a_2E0,V1b_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Ereal__sub_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).
tff(thm_2Efloat_2EFLOAT__MUL__RELATIVE,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0))
& p(c_2Efloat_2Enormalizes_2E1(c_2Erealax_2Ereal__mul_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)))) )
=> ( p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__mul_2E2(V0a_2E0,V1b_2E0)))
& ? [V2e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V2e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
& ( c_2Eieee_2EVal_2E1(c_2Eieee_2Efloat__mul_2E2(V0a_2E0,V1b_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Erealax_2Ereal__mul_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).
tff(thm_2Efloat_2EFLOAT__DIV__RELATIVE,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] :
( ( p(c_2Eieee_2EFinite_2E1(V0a_2E0))
& p(c_2Eieee_2EFinite_2E1(V1b_2E0))
& ~ p(c_2Eieee_2EIszero_2E1(V1b_2E0))
& p(c_2Efloat_2Enormalizes_2E1(c_2Ereal_2E_2F_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)))) )
=> ( p(c_2Eieee_2EFinite_2E1(c_2Eieee_2Efloat__div_2E2(V0a_2E0,V1b_2E0)))
& ? [V2e_2E0: tyop_2Erealax_2Ereal] :
( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(V2e_2E0),c_2Ereal_2E_2F_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ereal_2Epow_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))))
& ( c_2Eieee_2EVal_2E1(c_2Eieee_2Efloat__div_2E2(V0a_2E0,V1b_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2E_2F_2E2(c_2Eieee_2EVal_2E1(V0a_2E0),c_2Eieee_2EVal_2E1(V1b_2E0)),c_2Erealax_2Ereal__add_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).
%------------------------------------------------------------------------------