ITP001 Axioms: ITP136_7.ax
%------------------------------------------------------------------------------
% File : ITP136_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 : ieee.ax [Gau19]
% : HL4136_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 583 ( 205 unt; 293 typ; 0 def)
% Number of atoms : 591 ( 403 equ)
% Maximal formula atoms : 23 ( 1 avg)
% Number of connectives : 320 ( 19 ~; 38 |; 108 &)
% ( 80 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 240 ( 136 >; 104 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 286 ( 286 usr; 132 con; 0-6 aty)
% Number of variables : 845 ( 783 !; 15 ?; 845 :)
% ( 47 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Eieee_2Eccode,type,
tyop_2Eieee_2Eccode: $tType ).
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_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ereal_2E_2F_2E0,type,
c_2Ereal_2E_2F_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2E_2F_2E2,type,
c_2Ereal_2E_2F_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3E_3D_2E0,type,
c_2Earithmetic_2E_3E_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3E_3D_2E2,type,
c_2Earithmetic_2E_3E_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > 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_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
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_2Ebool_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EEVEN_2E0,type,
c_2Earithmetic_2EEVEN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EEVEN_2E1,type,
c_2Earithmetic_2EEVEN_2E1: tyop_2Enum_2Enum > 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_2Eieee_2EEq_2E0,type,
c_2Eieee_2EEq_2E0: tyop_2Eieee_2Eccode ).
tff(c_2Eieee_2EExponent_2E0,type,
c_2Eieee_2EExponent_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Enum_2Enum) ).
tff(c_2Eieee_2EExponent_2E1,type,
c_2Eieee_2EExponent_2E1: tyop_2Eieee_2Efloat > tyop_2Enum_2Enum ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
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_2Eieee_2EFloat_2E0,type,
c_2Eieee_2EFloat_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eieee_2Efloat) ).
tff(c_2Eieee_2EFloat_2E1,type,
c_2Eieee_2EFloat_2E1: tyop_2Erealax_2Ereal > tyop_2Eieee_2Efloat ).
tff(c_2Eieee_2EFraction_2E0,type,
c_2Eieee_2EFraction_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Enum_2Enum) ).
tff(c_2Eieee_2EFraction_2E1,type,
c_2Eieee_2EFraction_2E1: tyop_2Eieee_2Efloat > tyop_2Enum_2Enum ).
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_2Eieee_2EGt_2E0,type,
c_2Eieee_2EGt_2E0: tyop_2Eieee_2Eccode ).
tff(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
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_2EIsintegral_2E0,type,
c_2Eieee_2EIsintegral_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2EIsintegral_2E1,type,
c_2Eieee_2EIsintegral_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_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Eieee_2ELt_2E0,type,
c_2Eieee_2ELt_2E0: tyop_2Eieee_2Eccode ).
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_2Eieee_2EROUNDFLOAT_2E0,type,
c_2Eieee_2EROUNDFLOAT_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat) ).
tff(c_2Eieee_2EROUNDFLOAT_2E1,type,
c_2Eieee_2EROUNDFLOAT_2E1: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).
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_2Eieee_2ESign_2E0,type,
c_2Eieee_2ESign_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Enum_2Enum) ).
tff(c_2Eieee_2ESign_2E1,type,
c_2Eieee_2ESign_2E1: tyop_2Eieee_2Efloat > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eieee_2ETo__nearest_2E0,type,
c_2Eieee_2ETo__nearest_2E0: tyop_2Eieee_2Eroundmode ).
tff(c_2Eieee_2ETo__ninfinity_2E0,type,
c_2Eieee_2ETo__ninfinity_2E0: tyop_2Eieee_2Eroundmode ).
tff(c_2Eieee_2ETo__pinfinity_2E0,type,
c_2Eieee_2ETo__pinfinity_2E0: tyop_2Eieee_2Eroundmode ).
tff(c_2Eieee_2EUlp_2E0,type,
c_2Eieee_2EUlp_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Erealax_2Ereal) ).
tff(c_2Eieee_2EUlp_2E1,type,
c_2Eieee_2EUlp_2E1: tyop_2Eieee_2Efloat > tyop_2Erealax_2Ereal ).
tff(c_2Eieee_2EUn_2E0,type,
c_2Eieee_2EUn_2E0: tyop_2Eieee_2Eccode ).
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_2Eccode2num_2E0,type,
c_2Eieee_2Eccode2num_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Eccode2num_2E1,type,
c_2Eieee_2Eccode2num_2E1: tyop_2Eieee_2Eccode > tyop_2Enum_2Enum ).
tff(c_2Eieee_2Eccode__CASE_2E0,type,
c_2Eieee_2Eccode__CASE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))))) ).
tff(c_2Eieee_2Eccode__CASE_2E5,type,
c_2Eieee_2Eccode__CASE_2E5:
!>[A_27a: $tType] : ( ( tyop_2Eieee_2Eccode * A_27a * A_27a * A_27a * A_27a ) > A_27a ) ).
tff(c_2Eieee_2Eccode__size_2E0,type,
c_2Eieee_2Eccode__size_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Eccode__size_2E1,type,
c_2Eieee_2Eccode__size_2E1: tyop_2Eieee_2Eccode > 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_2Eieee_2Eencoding_2E0,type,
c_2Eieee_2Eencoding_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_2Enum_2Enum)) ).
tff(c_2Eieee_2Eencoding_2E2,type,
c_2Eieee_2Eencoding_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_2Enum_2Enum ).
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_2Efadd_2E0,type,
c_2Eieee_2Efadd_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))) ).
tff(c_2Eieee_2Efadd_2E4,type,
c_2Eieee_2Efadd_2E4: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Eieee_2Eroundmode * 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)) ) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Efcompare_2E0,type,
c_2Eieee_2Efcompare_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Eieee_2Eccode))) ).
tff(c_2Eieee_2Efcompare_2E3,type,
c_2Eieee_2Efcompare_2E3: ( 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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ) > tyop_2Eieee_2Eccode ).
tff(c_2Eieee_2Efdiv_2E0,type,
c_2Eieee_2Efdiv_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))) ).
tff(c_2Eieee_2Efdiv_2E4,type,
c_2Eieee_2Efdiv_2E4: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Eieee_2Eroundmode * 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)) ) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Efeq_2E0,type,
c_2Eieee_2Efeq_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))) ).
tff(c_2Eieee_2Efeq_2E3,type,
c_2Eieee_2Efeq_2E3: ( 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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Efge_2E0,type,
c_2Eieee_2Efge_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))) ).
tff(c_2Eieee_2Efge_2E3,type,
c_2Eieee_2Efge_2E3: ( 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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Efgt_2E0,type,
c_2Eieee_2Efgt_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))) ).
tff(c_2Eieee_2Efgt_2E3,type,
c_2Eieee_2Efgt_2E3: ( 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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Efintrnd_2E0,type,
c_2Eieee_2Efintrnd_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,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_2Efintrnd_2E3,type,
c_2Eieee_2Efintrnd_2E3: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Eieee_2Eroundmode * 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_2Efle_2E0,type,
c_2Eieee_2Efle_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))) ).
tff(c_2Eieee_2Efle_2E3,type,
c_2Eieee_2Efle_2E3: ( 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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ) > tyop_2Emin_2Ebool ).
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__To__zero_2E0,type,
c_2Eieee_2Efloat__To__zero_2E0: tyop_2Eieee_2Eroundmode ).
tff(c_2Eieee_2Efloat__abs_2E0,type,
c_2Eieee_2Efloat__abs_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat) ).
tff(c_2Eieee_2Efloat__abs_2E1,type,
c_2Eieee_2Efloat__abs_2E1: tyop_2Eieee_2Efloat > 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__neg_2E0,type,
c_2Eieee_2Efloat__neg_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat) ).
tff(c_2Eieee_2Efloat__neg_2E1,type,
c_2Eieee_2Efloat__neg_2E1: tyop_2Eieee_2Efloat > tyop_2Eieee_2Efloat ).
tff(c_2Eieee_2Efloat__rem_2E0,type,
c_2Eieee_2Efloat__rem_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat)) ).
tff(c_2Eieee_2Efloat__rem_2E2,type,
c_2Eieee_2Efloat__rem_2E2: ( tyop_2Eieee_2Efloat * tyop_2Eieee_2Efloat ) > tyop_2Eieee_2Efloat ).
tff(c_2Eieee_2Efloat__sqrt_2E0,type,
c_2Eieee_2Efloat__sqrt_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat) ).
tff(c_2Eieee_2Efloat__sqrt_2E1,type,
c_2Eieee_2Efloat__sqrt_2E1: 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_2Eflt_2E0,type,
c_2Eieee_2Eflt_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))) ).
tff(c_2Eieee_2Eflt_2E3,type,
c_2Eieee_2Eflt_2E3: ( 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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Efmul_2E0,type,
c_2Eieee_2Efmul_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))) ).
tff(c_2Eieee_2Efmul_2E4,type,
c_2Eieee_2Efmul_2E4: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Eieee_2Eroundmode * 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)) ) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Efneg_2E0,type,
c_2Eieee_2Efneg_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,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_2Efneg_2E3,type,
c_2Eieee_2Efneg_2E3: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Eieee_2Eroundmode * 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_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_2Eieee_2Efrem_2E0,type,
c_2Eieee_2Efrem_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))) ).
tff(c_2Eieee_2Efrem_2E4,type,
c_2Eieee_2Efrem_2E4: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Eieee_2Eroundmode * 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)) ) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Efsqrt_2E0,type,
c_2Eieee_2Efsqrt_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,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_2Efsqrt_2E3,type,
c_2Eieee_2Efsqrt_2E3: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Eieee_2Eroundmode * 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_2Efsub_2E0,type,
c_2Eieee_2Efsub_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))) ).
tff(c_2Eieee_2Efsub_2E4,type,
c_2Eieee_2Efsub_2E4: ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) * tyop_2Eieee_2Eroundmode * 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)) ) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Eieee_2Eintround_2E0,type,
c_2Eieee_2Eintround_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_2Eintround_2E3,type,
c_2Eieee_2Eintround_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_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__denormal_2E0,type,
c_2Eieee_2Eis__denormal_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__denormal_2E2,type,
c_2Eieee_2Eis__denormal_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__double_2E0,type,
c_2Eieee_2Eis__double_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2Eis__double_2E1,type,
c_2Eieee_2Eis__double_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Eis__double__extended_2E0,type,
c_2Eieee_2Eis__double__extended_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2Eis__double__extended_2E1,type,
c_2Eieee_2Eis__double__extended_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > 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__infinity_2E0,type,
c_2Eieee_2Eis__infinity_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__infinity_2E2,type,
c_2Eieee_2Eis__infinity_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__integral_2E0,type,
c_2Eieee_2Eis__integral_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__integral_2E2,type,
c_2Eieee_2Eis__integral_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__nan_2E0,type,
c_2Eieee_2Eis__nan_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__nan_2E2,type,
c_2Eieee_2Eis__nan_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__normal_2E0,type,
c_2Eieee_2Eis__normal_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__normal_2E2,type,
c_2Eieee_2Eis__normal_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__single_2E0,type,
c_2Eieee_2Eis__single_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2Eis__single_2E1,type,
c_2Eieee_2Eis__single_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Emin_2Ebool ).
tff(c_2Eieee_2Eis__single__extended_2E0,type,
c_2Eieee_2Eis__single__extended_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool) ).
tff(c_2Eieee_2Eis__single__extended_2E1,type,
c_2Eieee_2Eis__single__extended_2E1: 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_2E1,type,
c_2Eieee_2Eis__valid_2E1: 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_2Eis__zero_2E0,type,
c_2Eieee_2Eis__zero_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__zero_2E2,type,
c_2Eieee_2Eis__zero_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_2E0,type,
c_2Eieee_2Eminus_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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))) ).
tff(c_2Eieee_2Eminus_2E2,type,
c_2Eieee_2Eminus_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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
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_2Eieee_2Enum2ccode_2E0,type,
c_2Eieee_2Enum2ccode_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eieee_2Eccode) ).
tff(c_2Eieee_2Enum2ccode_2E1,type,
c_2Eieee_2Enum2ccode_2E1: tyop_2Enum_2Enum > tyop_2Eieee_2Eccode ).
tff(c_2Eieee_2Enum2roundmode_2E0,type,
c_2Eieee_2Enum2roundmode_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eieee_2Eroundmode) ).
tff(c_2Eieee_2Enum2roundmode_2E1,type,
c_2Eieee_2Enum2roundmode_2E1: tyop_2Enum_2Enum > tyop_2Eieee_2Eroundmode ).
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_2Erem_2E0,type,
c_2Eieee_2Erem_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Eieee_2Erem_2E2,type,
c_2Eieee_2Erem_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_2Eroundmode2num_2E0,type,
c_2Eieee_2Eroundmode2num_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Eroundmode2num_2E1,type,
c_2Eieee_2Eroundmode2num_2E1: tyop_2Eieee_2Eroundmode > tyop_2Enum_2Enum ).
tff(c_2Eieee_2Eroundmode__CASE_2E0,type,
c_2Eieee_2Eroundmode__CASE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))))) ).
tff(c_2Eieee_2Eroundmode__CASE_2E5,type,
c_2Eieee_2Eroundmode__CASE_2E5:
!>[A_27a: $tType] : ( ( tyop_2Eieee_2Eroundmode * A_27a * A_27a * A_27a * A_27a ) > A_27a ) ).
tff(c_2Eieee_2Eroundmode__size_2E0,type,
c_2Eieee_2Eroundmode__size_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Eroundmode__size_2E1,type,
c_2Eieee_2Eroundmode__size_2E1: tyop_2Eieee_2Eroundmode > 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_2Esome__nan_2E0,type,
c_2Eieee_2Esome__nan_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_2Esome__nan_2E1,type,
c_2Eieee_2Esome__nan_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_2Etransc_2Esqrt_2E0,type,
c_2Etransc_2Esqrt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Etransc_2Esqrt_2E1,type,
c_2Etransc_2Esqrt_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_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_2Eulp_2E0,type,
c_2Eieee_2Eulp_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_2Eulp_2E2,type,
c_2Eieee_2Eulp_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_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_2E1,type,
c_2Eieee_2Evalof_2E1: 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_2Ewordlength_2E0,type,
c_2Eieee_2Ewordlength_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).
tff(c_2Eieee_2Ewordlength_2E1,type,
c_2Eieee_2Ewordlength_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum ).
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_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_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_2A_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0,X1_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)),app_2E2(tyop_2Enum_2Enum,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))),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),X1_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_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2E_2F_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2E_2F_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2E_2F_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_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_3E_3D_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_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Emin_2E_40_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_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_2Emin_2E_40_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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Emin_2E_40_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),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_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ebool_2ECOND_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eieee_2Eccode,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eieee_2Eccode,X2_2E0: tyop_2Eieee_2Eccode] : ( c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Eccode,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eieee_2Eccode,tyop_2Eieee_2Eccode,app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Eieee_2Eccode),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Eieee_2Eccode)),c_2Ebool_2ECOND_2E0(tyop_2Eieee_2Eccode),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eieee_2Efloat,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eieee_2Efloat,X2_2E0: tyop_2Eieee_2Efloat] : ( c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Efloat,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat,app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat)),c_2Ebool_2ECOND_2E0(tyop_2Eieee_2Efloat),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0),X1_2E0),X2_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(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E0,X0_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_2Eieee_2EExponent_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EExponent_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Enum_2Enum,c_2Eieee_2EExponent_2E0,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_2Eieee_2EFloat_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2EFloat_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Eieee_2Efloat,c_2Eieee_2EFloat_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2EFraction_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EFraction_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Enum_2Enum,c_2Eieee_2EFraction_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(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),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_2EIsintegral_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EIsintegral_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool,c_2Eieee_2EIsintegral_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(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ebool_2ELET_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ebool_2ELET_2E0(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),X1_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_2Eieee_2EROUNDFLOAT_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EROUNDFLOAT_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat,c_2Eieee_2EROUNDFLOAT_2E0,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_2ESign_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2ESign_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Enum_2Enum,c_2Eieee_2ESign_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eieee_2Eccode,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Enum_2Enum)] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Enum_2Enum,tyop_2Eieee_2Eccode,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Enum_2Enum,tyop_2Eieee_2Eccode),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eieee_2Eroundmode,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Enum_2Enum)] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Enum_2Enum,tyop_2Eieee_2Eroundmode,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Enum_2Enum,tyop_2Eieee_2Eroundmode),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Eieee_2Efloat,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Eieee_2Efloat,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,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_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Eieee_2Efloat),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2EUlp_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EUlp_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Erealax_2Ereal,c_2Eieee_2EUlp_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(arityeq1_2Ec_2Eieee_2Eccode2num_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Eccode] : ( c_2Eieee_2Eccode2num_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Eccode,tyop_2Enum_2Enum,c_2Eieee_2Eccode2num_2E0,X0_2E0) ) ).
tff(arityeq5_2Ec_2Eieee_2Eccode__CASE_2E5_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eieee_2Eccode,X1_2E0: A_27a,X2_2E0: A_27a,X3_2E0: A_27a,X4_2E0: A_27a] : ( c_2Eieee_2Eccode__CASE_2E5(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Eieee_2Eccode__CASE_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eccode__size_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Eccode] : ( c_2Eieee_2Eccode__size_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Eccode,tyop_2Enum_2Enum,c_2Eieee_2Eccode__size_2E0,X0_2E0) ) ).
tff(arityeq4_2Ec_2Eieee_2Eclosest_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X3_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eclosest_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Erealax_2Ereal,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),app_2E2(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)),app_2E2(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))),c_2Eieee_2Eclosest_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_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(arityeq4_2Ec_2Eieee_2Eclosest_2E4_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X3_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eclosest_2E4(tyop_2Erealax_2Ereal,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),c_2Eieee_2Eclosest_2E0(tyop_2Erealax_2Ereal),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(arityeq2_2Ec_2Eieee_2Eencoding_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_2Eencoding_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum),c_2Eieee_2Eencoding_2E0,X0_2E0),X1_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(arityeq4_2Ec_2Eieee_2Efadd_2E4,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eieee_2Eroundmode,X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efadd_2E4(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_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_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_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),c_2Eieee_2Efadd_2E0,X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Efcompare_2E3,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)),X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efcompare_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_2Eieee_2Eccode,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Eieee_2Eccode),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Eieee_2Eccode)),c_2Eieee_2Efcompare_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Eieee_2Efdiv_2E4,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eieee_2Eroundmode,X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efdiv_2E4(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_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_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_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),c_2Eieee_2Efdiv_2E0,X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Efeq_2E3,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)),X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efeq_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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eieee_2Efeq_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Efge_2E3,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)),X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efge_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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eieee_2Efge_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Efgt_2E3,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)),X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efgt_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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eieee_2Efgt_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Efintrnd_2E3,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eieee_2Eroundmode,X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efintrnd_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_2Eieee_2Eroundmode,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_2Eieee_2Eroundmode,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_2Efintrnd_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Efle_2E3,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)),X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efle_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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eieee_2Efle_2E0,X0_2E0),X1_2E0),X2_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(arityeq1_2Ec_2Eieee_2Efloat__abs_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__abs_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__abs_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(arityeq1_2Ec_2Eieee_2Efloat__neg_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__neg_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__neg_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Efloat__rem_2E2,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat,X1_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__rem_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__rem_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Efloat__sqrt_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__sqrt_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__sqrt_2E0,X0_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(arityeq3_2Ec_2Eieee_2Eflt_2E3,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)),X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Eflt_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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eieee_2Eflt_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Eieee_2Efmul_2E4,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eieee_2Eroundmode,X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efmul_2E4(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_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_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_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),c_2Eieee_2Efmul_2E0,X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Efneg_2E3,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eieee_2Eroundmode,X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efneg_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_2Eieee_2Eroundmode,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_2Eieee_2Eroundmode,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_2Efneg_2E0,X0_2E0),X1_2E0),X2_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(arityeq4_2Ec_2Eieee_2Efrem_2E4,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eieee_2Eroundmode,X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efrem_2E4(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_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_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_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),c_2Eieee_2Efrem_2E0,X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Efsqrt_2E3,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eieee_2Eroundmode,X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efsqrt_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_2Eieee_2Eroundmode,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_2Eieee_2Eroundmode,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_2Efsqrt_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Eieee_2Efsub_2E4,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eieee_2Eroundmode,X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efsub_2E4(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_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_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_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),c_2Eieee_2Efsub_2E0,X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Eieee_2Eintround_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_2Eintround_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_2Eintround_2E0,X0_2E0),X1_2E0),X2_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_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Erealax_2Ereal,X3_2E0: A_27a] : ( c_2Eieee_2Eis__closest_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(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))),c_2Eieee_2Eis__closest_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Eis__denormal_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__denormal_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__denormal_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eis__double_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eis__double_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Eieee_2Eis__double_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eis__double__extended_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eis__double__extended_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Eieee_2Eis__double__extended_2E0,X0_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__infinity_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__infinity_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__infinity_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Eis__integral_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__integral_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__integral_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Eis__nan_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__nan_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__nan_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eieee_2Eis__normal_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__normal_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__normal_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eis__single_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eis__single_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Eieee_2Eis__single_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eis__single__extended_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eis__single__extended_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Eieee_2Eis__single__extended_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eis__valid_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eis__valid_2E1(X0_2E0) = 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) ) ).
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(arityeq2_2Ec_2Eieee_2Eis__zero_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__zero_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__zero_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(arityeq2_2Ec_2Eieee_2Eminus_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_2Eminus_2E2(X0_2E0,X1_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_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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Eieee_2Eminus_2E0,X0_2E0),X1_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_2Eieee_2Enum2ccode_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Enum2ccode_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eieee_2Eccode,c_2Eieee_2Enum2ccode_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Enum2roundmode_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Enum2roundmode_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eieee_2Eroundmode,c_2Eieee_2Enum2roundmode_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(arityeq2_2Ec_2Eieee_2Erem_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Erem_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_2Eieee_2Erem_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_2Eroundmode2num_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Eroundmode] : ( c_2Eieee_2Eroundmode2num_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Enum_2Enum,c_2Eieee_2Eroundmode2num_2E0,X0_2E0) ) ).
tff(arityeq5_2Ec_2Eieee_2Eroundmode__CASE_2E5_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eieee_2Eroundmode,X1_2E0: A_27a,X2_2E0: A_27a,X3_2E0: A_27a,X4_2E0: A_27a] : ( c_2Eieee_2Eroundmode__CASE_2E5(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Eieee_2Eroundmode__CASE_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Eroundmode__size_2E1,axiom,
! [X0_2E0: tyop_2Eieee_2Eroundmode] : ( c_2Eieee_2Eroundmode__size_2E1(X0_2E0) = app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Enum_2Enum,c_2Eieee_2Eroundmode__size_2E0,X0_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_2Esome__nan_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Esome__nan_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_2Esome__nan_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Etransc_2Esqrt_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Etransc_2Esqrt_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Etransc_2Esqrt_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_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_2Eulp_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_2Eulp_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_2Eulp_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eieee_2Evalof_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Evalof_2E1(X0_2E0) = 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) ) ).
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(arityeq1_2Ec_2Eieee_2Ewordlength_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Ewordlength_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Eieee_2Ewordlength_2E0,X0_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_2Eieee_2Eexpwidth,axiom,
! [V0ew_2E0: tyop_2Enum_2Enum,V1fw_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Eexpwidth_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0ew_2E0,V1fw_2E0)) = V0ew_2E0 ) ).
tff(thm_2Eieee_2Efracwidth,axiom,
! [V0ew_2E0: tyop_2Enum_2Enum,V1fw_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Efracwidth_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0ew_2E0,V1fw_2E0)) = V1fw_2E0 ) ).
tff(thm_2Eieee_2Ewordlength,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Ewordlength_2E1(V0X_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(c_2Eieee_2Eexpwidth_2E1(V0X_2E0),c_2Eieee_2Efracwidth_2E1(V0X_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ).
tff(thm_2Eieee_2Eemax,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eemax_2E1(V0X_2E0) = c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eieee_2Eexpwidth_2E1(V0X_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ).
tff(thm_2Eieee_2Ebias,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Ebias_2E1(V0X_2E0) = c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2D_2E2(c_2Eieee_2Eexpwidth_2E1(V0X_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ).
tff(thm_2Eieee_2Eis__single,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( p(c_2Eieee_2Eis__single_2E1(V0X_2E0))
<=> ( ( c_2Eieee_2Eexpwidth_2E1(V0X_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
& ( c_2Eieee_2Ewordlength_2E1(V0X_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_2EZERO_2E0)))))) ) ) ) ).
tff(thm_2Eieee_2Eis__double,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( p(c_2Eieee_2Eis__double_2E1(V0X_2E0))
<=> ( ( c_2Eieee_2Eexpwidth_2E1(V0X_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) )
& ( c_2Eieee_2Ewordlength_2E1(V0X_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_2EZERO_2E0))))))) ) ) ) ).
tff(thm_2Eieee_2Eis__single__extended,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( p(c_2Eieee_2Eis__single__extended_2E1(V0X_2E0))
<=> ( p(c_2Earithmetic_2E_3E_3D_2E2(c_2Eieee_2Eexpwidth_2E1(V0X_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))
& p(c_2Earithmetic_2E_3E_3D_2E2(c_2Eieee_2Ewordlength_2E1(V0X_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) ) ).
tff(thm_2Eieee_2Eis__double__extended,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( p(c_2Eieee_2Eis__double__extended_2E1(V0X_2E0))
<=> ( p(c_2Earithmetic_2E_3E_3D_2E2(c_2Eieee_2Eexpwidth_2E1(V0X_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))
& p(c_2Earithmetic_2E_3E_3D_2E2(c_2Eieee_2Ewordlength_2E1(V0X_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))) ) ) ).
tff(thm_2Eieee_2Esign,axiom,
! [V0s_2E0: tyop_2Enum_2Enum,V1e_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Esign_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0s_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1e_2E0,V2f_2E0))) = V0s_2E0 ) ).
tff(thm_2Eieee_2Eexponent,axiom,
! [V0s_2E0: tyop_2Enum_2Enum,V1e_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Eexponent_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0s_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1e_2E0,V2f_2E0))) = V1e_2E0 ) ).
tff(thm_2Eieee_2Efraction,axiom,
! [V0s_2E0: tyop_2Enum_2Enum,V1e_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Efraction_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0s_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1e_2E0,V2f_2E0))) = V2f_2E0 ) ).
tff(thm_2Eieee_2Eis__nan,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__nan_2E2(V0X_2E0,V1a_2E0))
<=> ( ( c_2Eieee_2Eexponent_2E1(V1a_2E0) = c_2Eieee_2Eemax_2E1(V0X_2E0) )
& ( c_2Eieee_2Efraction_2E1(V1a_2E0) != c_2Enum_2E0_2E0 ) ) ) ).
tff(thm_2Eieee_2Eis__infinity,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__infinity_2E2(V0X_2E0,V1a_2E0))
<=> ( ( c_2Eieee_2Eexponent_2E1(V1a_2E0) = c_2Eieee_2Eemax_2E1(V0X_2E0) )
& ( c_2Eieee_2Efraction_2E1(V1a_2E0) = c_2Enum_2E0_2E0 ) ) ) ).
tff(thm_2Eieee_2Eis__normal,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__normal_2E2(V0X_2E0,V1a_2E0))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Eieee_2Eexponent_2E1(V1a_2E0)))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Eexponent_2E1(V1a_2E0),c_2Eieee_2Eemax_2E1(V0X_2E0))) ) ) ).
tff(thm_2Eieee_2Eis__denormal,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__denormal_2E2(V0X_2E0,V1a_2E0))
<=> ( ( c_2Eieee_2Eexponent_2E1(V1a_2E0) = c_2Enum_2E0_2E0 )
& ( c_2Eieee_2Efraction_2E1(V1a_2E0) != c_2Enum_2E0_2E0 ) ) ) ).
tff(thm_2Eieee_2Eis__zero,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__zero_2E2(V0X_2E0,V1a_2E0))
<=> ( ( c_2Eieee_2Eexponent_2E1(V1a_2E0) = c_2Enum_2E0_2E0 )
& ( c_2Eieee_2Efraction_2E1(V1a_2E0) = c_2Enum_2E0_2E0 ) ) ) ).
tff(thm_2Eieee_2Eis__valid,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1s_2E0: tyop_2Enum_2Enum,V2e_2E0: tyop_2Enum_2Enum,V3f_2E0: tyop_2Enum_2Enum] :
( p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1s_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2e_2E0,V3f_2E0))))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(V1s_2E0,c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0))))
& p(c_2Eprim__rec_2E_3C_2E2(V2e_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(V3f_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_2Eieee_2Eis__finite,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__finite_2E2(V0X_2E0,V1a_2E0))
<=> ( p(c_2Eieee_2Eis__valid_2E2(V0X_2E0,V1a_2E0))
& ( p(c_2Eieee_2Eis__normal_2E2(V0X_2E0,V1a_2E0))
| p(c_2Eieee_2Eis__denormal_2E2(V0X_2E0,V1a_2E0))
| p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V1a_2E0)) ) ) ) ).
tff(thm_2Eieee_2Eplus__infinity,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eplus__infinity_2E1(V0X_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2E0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eieee_2Eemax_2E1(V0X_2E0),c_2Enum_2E0_2E0)) ) ).
tff(thm_2Eieee_2Eminus__infinity,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eminus__infinity_2E1(V0X_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eieee_2Eemax_2E1(V0X_2E0),c_2Enum_2E0_2E0)) ) ).
tff(thm_2Eieee_2Eplus__zero,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eplus__zero_2E1(V0X_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2E0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Enum_2E0_2E0)) ) ).
tff(thm_2Eieee_2Eminus__zero,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Eminus__zero_2E1(V0X_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Enum_2E0_2E0)) ) ).
tff(thm_2Eieee_2Etopfloat,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Etopfloat_2E1(V0X_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2E0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(c_2Eieee_2Eemax_2E1(V0X_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eieee_2Efracwidth_2E1(V0X_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).
tff(thm_2Eieee_2Ebottomfloat,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Ebottomfloat_2E1(V0X_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(c_2Eieee_2Eemax_2E1(V0X_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eieee_2Efracwidth_2E1(V0X_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).
tff(thm_2Eieee_2Eminus,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))] : ( c_2Eieee_2Eminus_2E2(V0X_2E0,V1a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eieee_2Esign_2E1(V1a_2E0)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E1(V1a_2E0),c_2Eieee_2Efraction_2E1(V1a_2E0))) ) ).
tff(thm_2Eieee_2Eencoding,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1s_2E0: tyop_2Enum_2Enum,V2e_2E0: tyop_2Enum_2Enum,V3f_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Eencoding_2E2(V0X_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1s_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2e_2E0,V3f_2E0))) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(V1s_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2D_2E2(c_2Eieee_2Ewordlength_2E1(V0X_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Earithmetic_2E_2A_2E2(V2e_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eieee_2Efracwidth_2E1(V0X_2E0)))),V3f_2E0) ) ).
tff(thm_2Eieee_2Evalof,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V2e_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2e_2E0))
<=> ( V2e_2E0 = c_2Enum_2E0_2E0 ) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1s_2E0: tyop_2Enum_2Enum,V2e_2E0: tyop_2Enum_2Enum,V3f_2E0: tyop_2Enum_2Enum] : ( c_2Eieee_2Evalof_2E2(V0X_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1s_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2e_2E0,V3f_2E0))) = c_2Ebool_2ECOND_2E3(tyop_2Erealax_2Ereal,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2e_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)))),V1s_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(V3f_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)))),V1s_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))),V2e_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(V3f_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_2Eieee_2Elargest,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Elargest_2E1(V0X_2E0) = c_2Erealax_2Ereal__mul_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))),c_2Earithmetic_2E_2D_2E2(c_2Eieee_2Eemax_2E1(V0X_2E0),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_2Eieee_2Ebias_2E1(V0X_2E0))),c_2Ereal_2Ereal__sub_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),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_2Eieee_2Efracwidth_2E1(V0X_2E0))))) ) ).
tff(thm_2Eieee_2Ethreshold,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Ethreshold_2E1(V0X_2E0) = c_2Erealax_2Ereal__mul_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))),c_2Earithmetic_2E_2D_2E2(c_2Eieee_2Eemax_2E1(V0X_2E0),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_2Eieee_2Ebias_2E1(V0X_2E0))),c_2Ereal_2Ereal__sub_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),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_2Enum_2ESUC_2E1(c_2Eieee_2Efracwidth_2E1(V0X_2E0)))))) ) ).
tff(thm_2Eieee_2Eulp,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))] : ( c_2Eieee_2Eulp_2E2(V0X_2E0,V1a_2E0) = c_2Ereal_2Ereal__sub_2E2(c_2Eieee_2Evalof_2E2(V0X_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2E0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E1(V1a_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Eieee_2Evalof_2E2(V0X_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2E0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E1(V1a_2E0),c_2Enum_2E0_2E0)))) ) ).
tff(thm_2Eieee_2Eroundmode__TY__DEF,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V1n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1n_2E0) = c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Enum_2Enum)] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Enum_2Enum,tyop_2Eieee_2Eroundmode,F0_2E0,V0rep_2E0)) ) ).
tff(thm_2Eieee_2Eroundmode__BIJ,axiom,
( ! [V0a_2E0: tyop_2Eieee_2Eroundmode] : ( c_2Eieee_2Enum2roundmode_2E1(c_2Eieee_2Eroundmode2num_2E1(V0a_2E0)) = V0a_2E0 )
& ! [V1r_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V1r_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
<=> ( c_2Eieee_2Eroundmode2num_2E1(c_2Eieee_2Enum2roundmode_2E1(V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Eieee_2Eroundmode__size__def,axiom,
! [V0x_2E0: tyop_2Eieee_2Eroundmode] : ( c_2Eieee_2Eroundmode__size_2E1(V0x_2E0) = c_2Enum_2E0_2E0 ) ).
tff(thm_2Eieee_2Eroundmode__CASE,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool)] :
( ! [V0x_2E0: tyop_2Eieee_2Eroundmode] :
( p(app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,F0_2E0,V0x_2E0))
<=> ( c_2Eieee_2Eroundmode2num_2E1(V0x_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)) ) )
=> ! [V0x_2E0: tyop_2Eieee_2Eroundmode,V1v0_2E0: A_27a,V2v1_2E0: A_27a,V3v2_2E0: A_27a,V4v3_2E0: A_27a] : ( c_2Eieee_2Eroundmode__CASE_2E5(A_27a,V0x_2E0,V1v0_2E0,V2v1_2E0,V3v2_2E0,V4v3_2E0) = c_2Ebool_2ECOND_2E3(A_27a,c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Eroundmode2num_2E1(V0x_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1v0_2E0,c_2Ebool_2ECOND_2E3(A_27a,c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Eroundmode2num_2E1(V0x_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V2v1_2E0,c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,F0_2E0,V0x_2E0),V3v2_2E0,V4v3_2E0))) ) ) ).
tff(thm_2Eieee_2Eis__closest,axiom,
! [A_27a: $tType,V0v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Erealax_2Ereal,V3a_2E0: A_27a] :
( p(c_2Eieee_2Eis__closest_2E4(A_27a,V0v_2E0,V1s_2E0,V2x_2E0,V3a_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3a_2E0,V1s_2E0))
& ! [V4b_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4b_2E0,V1s_2E0))
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(c_2Ereal_2Ereal__sub_2E2(app_2E2(A_27a,tyop_2Erealax_2Ereal,V0v_2E0,V3a_2E0),V2x_2E0)),c_2Ereal_2Eabs_2E1(c_2Ereal_2Ereal__sub_2E2(app_2E2(A_27a,tyop_2Erealax_2Ereal,V0v_2E0,V4b_2E0),V2x_2E0)))) ) ) ) ).
tff(thm_2Eieee_2Eclosest,axiom,
! [A_27a: $tType,F0_2E0: 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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))))] :
( ! [V0v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: tyop_2Erealax_2Ereal,V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4a_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V0v_2E0),V2s_2E0),V3x_2E0),V1p_2E0),V4a_2E0))
<=> ( p(c_2Eieee_2Eis__closest_2E4(A_27a,V0v_2E0,V2s_2E0,V3x_2E0,V4a_2E0))
& ( ? [V5b_2E0: A_27a] :
( p(c_2Eieee_2Eis__closest_2E4(A_27a,V0v_2E0,V2s_2E0,V3x_2E0,V5b_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1p_2E0,V5b_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1p_2E0,V4a_2E0)) ) ) )
=> ! [V0v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eclosest_2E4(A_27a,V0v_2E0,V1p_2E0,V2s_2E0,V3x_2E0) = c_2Emin_2E_40_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V0v_2E0),V2s_2E0),V3x_2E0),V1p_2E0)) ) ) ).
tff(thm_2Eieee_2Eround__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),F3_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),F10_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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F7_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))),F9_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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F5_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))),F8_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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F6_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))),F4_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)))] :
( ! [V2a_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_2Emin_2Ebool,F0_2E0,V2a_2E0) = c_2Earithmetic_2EEVEN_2E1(c_2Eieee_2Efraction_2E1(V2a_2E0)) )
=> ( ! [V14x_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_2Emin_2Ebool,F3_2E0,V14x_2E0) = c_2Ebool_2ET_2E0 )
=> ( ! [V10x_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_2Emin_2Ebool,F2_2E0,V10x_2E0) = c_2Ebool_2ET_2E0 )
=> ( ! [V6x_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_2Emin_2Ebool,F1_2E0,V6x_2E0) = c_2Ebool_2ET_2E0 )
=> ( ! [V12X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V15a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V13x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F10_2E0,V12X_2E0),V15a_2E0),V13x_2E0))
<=> ( p(c_2Eieee_2Eis__finite_2E2(V12X_2E0,V15a_2E0))
& p(c_2Ereal_2Ereal__lte_2E2(c_2Eieee_2Evalof_2E2(V12X_2E0,V15a_2E0),V13x_2E0)) ) )
=> ( ! [V12X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V13x_2E0: tyop_2Erealax_2Ereal,V15a_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F7_2E0,V12X_2E0),V13x_2E0),V15a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V15a_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F10_2E0,V12X_2E0),V15a_2E0),V13x_2E0)) )
=> ( ! [V4X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V7a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V5x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F9_2E0,V4X_2E0),V7a_2E0),V5x_2E0))
<=> ( p(c_2Eieee_2Eis__finite_2E2(V4X_2E0,V7a_2E0))
& p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(c_2Eieee_2Evalof_2E2(V4X_2E0,V7a_2E0)),c_2Ereal_2Eabs_2E1(V5x_2E0))) ) )
=> ( ! [V4X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V5x_2E0: tyop_2Erealax_2Ereal,V7a_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F5_2E0,V4X_2E0),V5x_2E0),V7a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V7a_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F9_2E0,V4X_2E0),V7a_2E0),V5x_2E0)) )
=> ( ! [V8X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V11a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V9x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F8_2E0,V8X_2E0),V11a_2E0),V9x_2E0))
<=> ( p(c_2Eieee_2Eis__finite_2E2(V8X_2E0,V11a_2E0))
& p(c_2Ereal_2Ereal__ge_2E2(c_2Eieee_2Evalof_2E2(V8X_2E0,V11a_2E0),V9x_2E0)) ) )
=> ( ! [V8X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V9x_2E0: tyop_2Erealax_2Ereal,V11a_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F6_2E0,V8X_2E0),V9x_2E0),V11a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V11a_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F8_2E0,V8X_2E0),V11a_2E0),V9x_2E0)) )
=> ( ! [V0X_2E0: 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))] : ( 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)),F4_2E0,V0X_2E0),V3a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V3a_2E0,c_2Eieee_2Eis__finite_2E2(V0X_2E0,V3a_2E0)) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eround_2E3(V0X_2E0,c_2Eieee_2ETo__nearest_2E0,V1x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ereal_2Ereal__lte_2E2(V1x_2E0,c_2Erealax_2Ereal__neg_2E1(c_2Eieee_2Ethreshold_2E1(V0X_2E0))),c_2Eieee_2Eminus__infinity_2E1(V0X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ereal_2Ereal__ge_2E2(V1x_2E0,c_2Eieee_2Ethreshold_2E1(V0X_2E0)),c_2Eieee_2Eplus__infinity_2E1(V0X_2E0),c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Evalof_2E1(V0X_2E0),F0_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)),F4_2E0,V0X_2E0)),V1x_2E0))) )
& ! [V4X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V5x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eround_2E3(V4X_2E0,c_2Eieee_2Efloat__To__zero_2E0,V5x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Erealax_2Ereal__lt_2E2(V5x_2E0,c_2Erealax_2Ereal__neg_2E1(c_2Eieee_2Elargest_2E1(V4X_2E0))),c_2Eieee_2Ebottomfloat_2E1(V4X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ereal_2Ereal__gt_2E2(V5x_2E0,c_2Eieee_2Elargest_2E1(V4X_2E0)),c_2Eieee_2Etopfloat_2E1(V4X_2E0),c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Evalof_2E1(V4X_2E0),F1_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F5_2E0,V4X_2E0),V5x_2E0)),V5x_2E0))) )
& ! [V8X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V9x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eround_2E3(V8X_2E0,c_2Eieee_2ETo__pinfinity_2E0,V9x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Erealax_2Ereal__lt_2E2(V9x_2E0,c_2Erealax_2Ereal__neg_2E1(c_2Eieee_2Elargest_2E1(V8X_2E0))),c_2Eieee_2Ebottomfloat_2E1(V8X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ereal_2Ereal__gt_2E2(V9x_2E0,c_2Eieee_2Elargest_2E1(V8X_2E0)),c_2Eieee_2Eplus__infinity_2E1(V8X_2E0),c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Evalof_2E1(V8X_2E0),F2_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F6_2E0,V8X_2E0),V9x_2E0)),V9x_2E0))) )
& ! [V12X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V13x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eround_2E3(V12X_2E0,c_2Eieee_2ETo__ninfinity_2E0,V13x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Erealax_2Ereal__lt_2E2(V13x_2E0,c_2Erealax_2Ereal__neg_2E1(c_2Eieee_2Elargest_2E1(V12X_2E0))),c_2Eieee_2Eminus__infinity_2E1(V12X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ereal_2Ereal__gt_2E2(V13x_2E0,c_2Eieee_2Elargest_2E1(V12X_2E0)),c_2Eieee_2Etopfloat_2E1(V12X_2E0),c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Evalof_2E1(V12X_2E0),F3_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F7_2E0,V12X_2E0),V13x_2E0)),V13x_2E0))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tff(thm_2Eieee_2Eis__integral,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__integral_2E2(V0X_2E0,V1a_2E0))
<=> ( p(c_2Eieee_2Eis__finite_2E2(V0X_2E0,V1a_2E0))
& ? [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Eabs_2E1(c_2Eieee_2Evalof_2E2(V0X_2E0,V1a_2E0)) = c_2Ereal_2Ereal__of__num_2E1(V2n_2E0) ) ) ) ).
tff(thm_2Eieee_2Eintround__def,axiom,
! [F3_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),F10_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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F7_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))),F9_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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F5_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))),F8_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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F6_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))),F4_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))),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_2Emin_2Ebool))] :
( ! [V15x_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_2Emin_2Ebool,F3_2E0,V15x_2E0) = c_2Ebool_2ET_2E0 )
=> ( ! [V11x_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_2Emin_2Ebool,F2_2E0,V11x_2E0) = c_2Ebool_2ET_2E0 )
=> ( ! [V7x_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_2Emin_2Ebool,F1_2E0,V7x_2E0) = c_2Ebool_2ET_2E0 )
=> ( ! [V13X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V16a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V14x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F10_2E0,V13X_2E0),V16a_2E0),V14x_2E0))
<=> ( p(c_2Eieee_2Eis__integral_2E2(V13X_2E0,V16a_2E0))
& p(c_2Ereal_2Ereal__lte_2E2(c_2Eieee_2Evalof_2E2(V13X_2E0,V16a_2E0),V14x_2E0)) ) )
=> ( ! [V13X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V14x_2E0: tyop_2Erealax_2Ereal,V16a_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F7_2E0,V13X_2E0),V14x_2E0),V16a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V16a_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F10_2E0,V13X_2E0),V16a_2E0),V14x_2E0)) )
=> ( ! [V5X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V8a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V6x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F9_2E0,V5X_2E0),V8a_2E0),V6x_2E0))
<=> ( p(c_2Eieee_2Eis__integral_2E2(V5X_2E0,V8a_2E0))
& p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Eabs_2E1(c_2Eieee_2Evalof_2E2(V5X_2E0,V8a_2E0)),c_2Ereal_2Eabs_2E1(V6x_2E0))) ) )
=> ( ! [V5X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V6x_2E0: tyop_2Erealax_2Ereal,V8a_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F5_2E0,V5X_2E0),V6x_2E0),V8a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V8a_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F9_2E0,V5X_2E0),V8a_2E0),V6x_2E0)) )
=> ( ! [V9X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V12a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V10x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F8_2E0,V9X_2E0),V12a_2E0),V10x_2E0))
<=> ( p(c_2Eieee_2Eis__integral_2E2(V9X_2E0,V12a_2E0))
& p(c_2Ereal_2Ereal__ge_2E2(c_2Eieee_2Evalof_2E2(V9X_2E0,V12a_2E0),V10x_2E0)) ) )
=> ( ! [V9X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V10x_2E0: tyop_2Erealax_2Ereal,V12a_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F6_2E0,V9X_2E0),V10x_2E0),V12a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool,V12a_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F8_2E0,V9X_2E0),V12a_2E0),V10x_2E0)) )
=> ( ! [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)),F4_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__integral_2E2(V0X_2E0,V4a_2E0)) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_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,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),F0_2E0,V0X_2E0),V2a_2E0))
<=> ? [V3n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2EEVEN_2E1(V3n_2E0))
& ( c_2Ereal_2Eabs_2E1(c_2Eieee_2Evalof_2E2(V0X_2E0,V2a_2E0)) = c_2Ereal_2Ereal__of__num_2E1(V3n_2E0) ) ) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eintround_2E3(V0X_2E0,c_2Eieee_2ETo__nearest_2E0,V1x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ereal_2Ereal__lte_2E2(V1x_2E0,c_2Erealax_2Ereal__neg_2E1(c_2Eieee_2Ethreshold_2E1(V0X_2E0))),c_2Eieee_2Eminus__infinity_2E1(V0X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ereal_2Ereal__ge_2E2(V1x_2E0,c_2Eieee_2Ethreshold_2E1(V0X_2E0)),c_2Eieee_2Eplus__infinity_2E1(V0X_2E0),c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Evalof_2E1(V0X_2E0),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),F0_2E0,V0X_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)),F4_2E0,V0X_2E0)),V1x_2E0))) )
& ! [V5X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V6x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eintround_2E3(V5X_2E0,c_2Eieee_2Efloat__To__zero_2E0,V6x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Erealax_2Ereal__lt_2E2(V6x_2E0,c_2Erealax_2Ereal__neg_2E1(c_2Eieee_2Elargest_2E1(V5X_2E0))),c_2Eieee_2Ebottomfloat_2E1(V5X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ereal_2Ereal__gt_2E2(V6x_2E0,c_2Eieee_2Elargest_2E1(V5X_2E0)),c_2Eieee_2Etopfloat_2E1(V5X_2E0),c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Evalof_2E1(V5X_2E0),F1_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F5_2E0,V5X_2E0),V6x_2E0)),V6x_2E0))) )
& ! [V9X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V10x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eintround_2E3(V9X_2E0,c_2Eieee_2ETo__pinfinity_2E0,V10x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Erealax_2Ereal__lt_2E2(V10x_2E0,c_2Erealax_2Ereal__neg_2E1(c_2Eieee_2Elargest_2E1(V9X_2E0))),c_2Eieee_2Ebottomfloat_2E1(V9X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ereal_2Ereal__gt_2E2(V10x_2E0,c_2Eieee_2Elargest_2E1(V9X_2E0)),c_2Eieee_2Eplus__infinity_2E1(V9X_2E0),c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Evalof_2E1(V9X_2E0),F2_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F6_2E0,V9X_2E0),V10x_2E0)),V10x_2E0))) )
& ! [V13X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V14x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Eintround_2E3(V13X_2E0,c_2Eieee_2ETo__ninfinity_2E0,V14x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Erealax_2Ereal__lt_2E2(V14x_2E0,c_2Erealax_2Ereal__neg_2E1(c_2Eieee_2Elargest_2E1(V13X_2E0))),c_2Eieee_2Eminus__infinity_2E1(V13X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ereal_2Ereal__gt_2E2(V14x_2E0,c_2Eieee_2Elargest_2E1(V13X_2E0)),c_2Eieee_2Etopfloat_2E1(V13X_2E0),c_2Eieee_2Eclosest_2E4(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Evalof_2E1(V13X_2E0),F3_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_2Erealax_2Ereal,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)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F7_2E0,V13X_2E0),V14x_2E0)),V14x_2E0))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tff(thm_2Eieee_2Esome__nan,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_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_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),F0_2E0,V0X_2E0),V1a_2E0) = c_2Eieee_2Eis__nan_2E2(V0X_2E0,V1a_2E0) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Eieee_2Esome__nan_2E1(V0X_2E0) = c_2Emin_2E_40_2E1(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_2Emin_2Ebool),F0_2E0,V0X_2E0)) ) ) ).
tff(thm_2Eieee_2Ezerosign,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V1s_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1s_2E0))
<=> ( V1s_2E0 = c_2Enum_2E0_2E0 ) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1s_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Ezerosign_2E3(V0X_2E0,V1s_2E0,V2a_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eis__zero_2E2(V0X_2E0,V2a_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1s_2E0),c_2Eieee_2Eplus__zero_2E1(V0X_2E0),c_2Eieee_2Eminus__zero_2E1(V0X_2E0)),V2a_2E0) ) ) ).
tff(thm_2Eieee_2Erem,axiom,
! [F3_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)))] :
( ! [V5x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,F3_2E0,V5x_2E0))
<=> ? [V6n_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Eabs_2E1(V5x_2E0) = c_2Ereal_2Ereal__of__num_2E1(V6n_2E0) ) )
=> ( ! [V5x_2E0: tyop_2Erealax_2Ereal] : ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F2_2E0,V5x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V5x_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,F3_2E0,V5x_2E0)) )
=> ( ! [V3x_2E0: tyop_2Erealax_2Ereal] :
( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,F1_2E0,V3x_2E0))
<=> ? [V4n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2EEVEN_2E1(V4n_2E0))
& ( c_2Ereal_2Eabs_2E1(V3x_2E0) = c_2Ereal_2Ereal__of__num_2E1(V4n_2E0) ) ) )
=> ( ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal,V2n_2E0: tyop_2Erealax_2Ereal] : ( 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_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0,V0x_2E0),V1y_2E0),V2n_2E0) = c_2Ereal_2Ereal__sub_2E2(V0x_2E0,c_2Erealax_2Ereal__mul_2E2(V2n_2E0,V1y_2E0)) )
=> ! [V0x_2E0: tyop_2Erealax_2Ereal,V1y_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2Erem_2E2(V0x_2E0,V1y_2E0) = c_2Ebool_2ELET_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0,V0x_2E0),V1y_2E0),c_2Eieee_2Eclosest_2E4(tyop_2Erealax_2Ereal,c_2Ecombin_2EI_2E0(tyop_2Erealax_2Ereal),F1_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,F2_2E0),c_2Ereal_2E_2F_2E2(V0x_2E0,V1y_2E0))) ) ) ) ) ) ).
tff(thm_2Eieee_2Efintrnd,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Eieee_2Eroundmode,V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efintrnd_2E3(V0X_2E0,V1m_2E0,V2a_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eis__nan_2E2(V0X_2E0,V2a_2E0),c_2Eieee_2Esome__nan_2E1(V0X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0),V2a_2E0,c_2Eieee_2Ezerosign_2E3(V0X_2E0,c_2Eieee_2Esign_2E1(V2a_2E0),c_2Eieee_2Eintround_2E3(V0X_2E0,V1m_2E0,c_2Eieee_2Evalof_2E2(V0X_2E0,V2a_2E0))))) ) ).
tff(thm_2Eieee_2Efadd,axiom,
! [F2_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool),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_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F1_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))] :
( ! [V1m_2E0: tyop_2Eieee_2Eroundmode] :
( p(app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,F2_2E0,V1m_2E0))
<=> ( V1m_2E0 = c_2Eieee_2ETo__ninfinity_2E0 ) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V2a_2E0),V3b_2E0))
<=> ( p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V2a_2E0))
| p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V3b_2E0))
| ( p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0))
& p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V3b_2E0))
& ( c_2Eieee_2Esign_2E1(V2a_2E0) != c_2Eieee_2Esign_2E1(V3b_2E0) ) ) ) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F1_2E0,V0X_2E0),V2a_2E0),V3b_2E0))
<=> ( p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V2a_2E0))
& p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V3b_2E0))
& ( c_2Eieee_2Esign_2E1(V2a_2E0) = c_2Eieee_2Esign_2E1(V3b_2E0) ) ) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Eieee_2Eroundmode,V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efadd_2E4(V0X_2E0,V1m_2E0,V2a_2E0,V3b_2E0) = c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V2a_2E0),V3b_2E0),c_2Eieee_2Esome__nan_2E1(V0X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0),V2a_2E0,c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V3b_2E0),V3b_2E0,c_2Eieee_2Ezerosign_2E3(V0X_2E0,c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,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_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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F1_2E0,V0X_2E0),V2a_2E0),V3b_2E0),c_2Eieee_2Esign_2E1(V2a_2E0),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,F2_2E0,V1m_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2E0_2E0)),c_2Eieee_2Eround_2E3(V0X_2E0,V1m_2E0,c_2Erealax_2Ereal__add_2E2(c_2Eieee_2Evalof_2E2(V0X_2E0,V2a_2E0),c_2Eieee_2Evalof_2E2(V0X_2E0,V3b_2E0))))))) ) ) ) ) ).
tff(thm_2Eieee_2Efsub,axiom,
! [F2_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool),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_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F1_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))] :
( ! [V1m_2E0: tyop_2Eieee_2Eroundmode] :
( p(app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,F2_2E0,V1m_2E0))
<=> ( V1m_2E0 = c_2Eieee_2ETo__ninfinity_2E0 ) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V2a_2E0),V3b_2E0))
<=> ( p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V2a_2E0))
| p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V3b_2E0))
| ( p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0))
& p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V3b_2E0))
& ( c_2Eieee_2Esign_2E1(V2a_2E0) = c_2Eieee_2Esign_2E1(V3b_2E0) ) ) ) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F1_2E0,V0X_2E0),V2a_2E0),V3b_2E0))
<=> ( p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V2a_2E0))
& p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V3b_2E0))
& ( c_2Eieee_2Esign_2E1(V2a_2E0) != c_2Eieee_2Esign_2E1(V3b_2E0) ) ) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Eieee_2Eroundmode,V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efsub_2E4(V0X_2E0,V1m_2E0,V2a_2E0,V3b_2E0) = c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V2a_2E0),V3b_2E0),c_2Eieee_2Esome__nan_2E1(V0X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0),V2a_2E0,c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V3b_2E0),c_2Eieee_2Eminus_2E2(V0X_2E0,V3b_2E0),c_2Eieee_2Ezerosign_2E3(V0X_2E0,c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,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_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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F1_2E0,V0X_2E0),V2a_2E0),V3b_2E0),c_2Eieee_2Esign_2E1(V2a_2E0),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,F2_2E0,V1m_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2E0_2E0)),c_2Eieee_2Eround_2E3(V0X_2E0,V1m_2E0,c_2Ereal_2Ereal__sub_2E2(c_2Eieee_2Evalof_2E2(V0X_2E0,V2a_2E0),c_2Eieee_2Evalof_2E2(V0X_2E0,V3b_2E0))))))) ) ) ) ) ).
tff(thm_2Eieee_2Efmul,axiom,
! [F2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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)),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_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F1_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))] :
( ! [V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),F2_2E0,V2a_2E0),V3b_2E0))
<=> ( c_2Eieee_2Esign_2E1(V2a_2E0) = c_2Eieee_2Esign_2E1(V3b_2E0) ) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V2a_2E0),V3b_2E0))
<=> ( p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V2a_2E0))
| p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V3b_2E0))
| ( p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V2a_2E0))
& p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V3b_2E0)) )
| ( p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0))
& p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V3b_2E0)) ) ) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F1_2E0,V0X_2E0),V2a_2E0),V3b_2E0))
<=> ( p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0))
| p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V3b_2E0)) ) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Eieee_2Eroundmode,V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efmul_2E4(V0X_2E0,V1m_2E0,V2a_2E0,V3b_2E0) = c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V2a_2E0),V3b_2E0),c_2Eieee_2Esome__nan_2E1(V0X_2E0),c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F1_2E0,V0X_2E0),V2a_2E0),V3b_2E0),c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),F2_2E0,V2a_2E0),V3b_2E0),c_2Eieee_2Eplus__infinity_2E1(V0X_2E0),c_2Eieee_2Eminus__infinity_2E1(V0X_2E0)),c_2Eieee_2Ezerosign_2E3(V0X_2E0,c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,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_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),F2_2E0,V2a_2E0),V3b_2E0),c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Eieee_2Eround_2E3(V0X_2E0,V1m_2E0,c_2Erealax_2Ereal__mul_2E2(c_2Eieee_2Evalof_2E2(V0X_2E0,V2a_2E0),c_2Eieee_2Evalof_2E2(V0X_2E0,V3b_2E0)))))) ) ) ) ) ).
tff(thm_2Eieee_2Efdiv,axiom,
! [F2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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)),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_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F1_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))] :
( ! [V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),F2_2E0,V2a_2E0),V3b_2E0))
<=> ( c_2Eieee_2Esign_2E1(V2a_2E0) = c_2Eieee_2Esign_2E1(V3b_2E0) ) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V2a_2E0),V3b_2E0))
<=> ( p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V2a_2E0))
| p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V3b_2E0))
| ( p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V2a_2E0))
& p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V3b_2E0)) )
| ( p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0))
& p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V3b_2E0)) ) ) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F1_2E0,V0X_2E0),V2a_2E0),V3b_2E0))
<=> ( p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0))
| p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V3b_2E0)) ) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Eieee_2Eroundmode,V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efdiv_2E4(V0X_2E0,V1m_2E0,V2a_2E0,V3b_2E0) = c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V2a_2E0),V3b_2E0),c_2Eieee_2Esome__nan_2E1(V0X_2E0),c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F1_2E0,V0X_2E0),V2a_2E0),V3b_2E0),c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),F2_2E0,V2a_2E0),V3b_2E0),c_2Eieee_2Eplus__infinity_2E1(V0X_2E0),c_2Eieee_2Eminus__infinity_2E1(V0X_2E0)),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V3b_2E0),c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),F2_2E0,V2a_2E0),V3b_2E0),c_2Eieee_2Eplus__zero_2E1(V0X_2E0),c_2Eieee_2Eminus__zero_2E1(V0X_2E0)),c_2Eieee_2Ezerosign_2E3(V0X_2E0,c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,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_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),F2_2E0,V2a_2E0),V3b_2E0),c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Eieee_2Eround_2E3(V0X_2E0,V1m_2E0,c_2Ereal_2E_2F_2E2(c_2Eieee_2Evalof_2E2(V0X_2E0,V2a_2E0),c_2Eieee_2Evalof_2E2(V0X_2E0,V3b_2E0))))))) ) ) ) ) ).
tff(thm_2Eieee_2Efsqrt,axiom,
! [F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),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_2Emin_2Ebool))] :
( ! [V2a_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,F1_2E0,V2a_2E0))
<=> ( c_2Eieee_2Esign_2E1(V2a_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) )
=> ( ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2a_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,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),F0_2E0,V0X_2E0),V2a_2E0))
<=> ( p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V2a_2E0))
| ( p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0))
& ( c_2Eieee_2Esign_2E1(V2a_2E0) = c_2Enum_2E0_2E0 ) ) ) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Eieee_2Eroundmode,V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efsqrt_2E3(V0X_2E0,V1m_2E0,V2a_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eis__nan_2E2(V0X_2E0,V2a_2E0),c_2Eieee_2Esome__nan_2E1(V0X_2E0),c_2Ebool_2ECOND_2E3(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_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),F0_2E0,V0X_2E0),V2a_2E0),V2a_2E0,c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,F1_2E0,V2a_2E0),c_2Eieee_2Esome__nan_2E1(V0X_2E0),c_2Eieee_2Ezerosign_2E3(V0X_2E0,c_2Eieee_2Esign_2E1(V2a_2E0),c_2Eieee_2Eround_2E3(V0X_2E0,V1m_2E0,c_2Etransc_2Esqrt_2E1(c_2Eieee_2Evalof_2E2(V0X_2E0,V2a_2E0))))))) ) ) ) ).
tff(thm_2Eieee_2Efrem,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_2Emin_2Efun(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),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V2a_2E0),V3b_2E0))
<=> ( p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V2a_2E0))
| p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V3b_2E0))
| p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V2a_2E0))
| p(c_2Eieee_2Eis__zero_2E2(V0X_2E0,V3b_2E0)) ) )
=> ! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Eieee_2Eroundmode,V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efrem_2E4(V0X_2E0,V1m_2E0,V2a_2E0,V3b_2E0) = c_2Ebool_2ECOND_2E3(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_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V2a_2E0),V3b_2E0),c_2Eieee_2Esome__nan_2E1(V0X_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V3b_2E0),V2a_2E0,c_2Eieee_2Ezerosign_2E3(V0X_2E0,c_2Eieee_2Esign_2E1(V2a_2E0),c_2Eieee_2Eround_2E3(V0X_2E0,V1m_2E0,c_2Eieee_2Erem_2E2(c_2Eieee_2Evalof_2E2(V0X_2E0,V2a_2E0),c_2Eieee_2Evalof_2E2(V0X_2E0,V3b_2E0)))))) ) ) ).
tff(thm_2Eieee_2Efneg,axiom,
! [V0X_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Eieee_2Eroundmode,V2a_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efneg_2E3(V0X_2E0,V1m_2E0,V2a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eieee_2Esign_2E1(V2a_2E0)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E1(V2a_2E0),c_2Eieee_2Efraction_2E1(V2a_2E0))) ) ).
tff(thm_2Eieee_2Eccode__TY__DEF,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V1n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1n_2E0) = c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Enum_2Enum)] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Enum_2Enum,tyop_2Eieee_2Eccode,F0_2E0,V0rep_2E0)) ) ).
tff(thm_2Eieee_2Eccode__BIJ,axiom,
( ! [V0a_2E0: tyop_2Eieee_2Eccode] : ( c_2Eieee_2Enum2ccode_2E1(c_2Eieee_2Eccode2num_2E1(V0a_2E0)) = V0a_2E0 )
& ! [V1r_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V1r_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
<=> ( c_2Eieee_2Eccode2num_2E1(c_2Eieee_2Enum2ccode_2E1(V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Eieee_2Eccode__size__def,axiom,
! [V0x_2E0: tyop_2Eieee_2Eccode] : ( c_2Eieee_2Eccode__size_2E1(V0x_2E0) = c_2Enum_2E0_2E0 ) ).
tff(thm_2Eieee_2Eccode__CASE,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool)] :
( ! [V0x_2E0: tyop_2Eieee_2Eccode] :
( p(app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool,F0_2E0,V0x_2E0))
<=> ( c_2Eieee_2Eccode2num_2E1(V0x_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)) ) )
=> ! [V0x_2E0: tyop_2Eieee_2Eccode,V1v0_2E0: A_27a,V2v1_2E0: A_27a,V3v2_2E0: A_27a,V4v3_2E0: A_27a] : ( c_2Eieee_2Eccode__CASE_2E5(A_27a,V0x_2E0,V1v0_2E0,V2v1_2E0,V3v2_2E0,V4v3_2E0) = c_2Ebool_2ECOND_2E3(A_27a,c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Eccode2num_2E1(V0x_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1v0_2E0,c_2Ebool_2ECOND_2E3(A_27a,c_2Eprim__rec_2E_3C_2E2(c_2Eieee_2Eccode2num_2E1(V0x_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V2v1_2E0,c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool,F0_2E0,V0x_2E0),V3v2_2E0,V4v3_2E0))) ) ) ).
tff(thm_2Eieee_2Efcompare,axiom,
! [F1_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)),F2_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)),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_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F3_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_2Efun(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))] :
( p(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),F1_2E0,V0X_2E0),V1a_2E0))
<=> ( p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V1a_2E0))
& ( c_2Eieee_2Esign_2E1(V1a_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_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))] :
( p(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),F2_2E0,V0X_2E0),V1a_2E0))
<=> ( p(c_2Eieee_2Eis__infinity_2E2(V0X_2E0,V1a_2E0))
& ( c_2Eieee_2Esign_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)),V2b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V1a_2E0),V2b_2E0))
<=> ( p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V1a_2E0))
| p(c_2Eieee_2Eis__nan_2E2(V0X_2E0,V2b_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)),V2b_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,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F3_2E0,V0X_2E0),V1a_2E0),V2b_2E0))
<=> ( c_2Eieee_2Evalof_2E2(V0X_2E0,V1a_2E0) = c_2Eieee_2Evalof_2E2(V0X_2E0,V2b_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)),V2b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eieee_2Efcompare_2E3(V0X_2E0,V1a_2E0,V2b_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Eccode,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_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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F0_2E0,V0X_2E0),V1a_2E0),V2b_2E0),c_2Eieee_2EUn_2E0,c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Eccode,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),F1_2E0,V0X_2E0),V1a_2E0),c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Eccode,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),F1_2E0,V0X_2E0),V2b_2E0),c_2Eieee_2EEq_2E0,c_2Eieee_2ELt_2E0),c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Eccode,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),F2_2E0,V0X_2E0),V1a_2E0),c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Eccode,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),F2_2E0,V0X_2E0),V2b_2E0),c_2Eieee_2EEq_2E0,c_2Eieee_2EGt_2E0),c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Eccode,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),F1_2E0,V0X_2E0),V2b_2E0),c_2Eieee_2EGt_2E0,c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Eccode,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),F2_2E0,V0X_2E0),V2b_2E0),c_2Eieee_2ELt_2E0,c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Eccode,c_2Erealax_2Ereal__lt_2E2(c_2Eieee_2Evalof_2E2(V0X_2E0,V1a_2E0),c_2Eieee_2Evalof_2E2(V0X_2E0,V2b_2E0)),c_2Eieee_2ELt_2E0,c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Eccode,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_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),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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),F3_2E0,V0X_2E0),V1a_2E0),V2b_2E0),c_2Eieee_2EEq_2E0,c_2Eieee_2EGt_2E0))))))) ) ) ) ) ) ).
tff(thm_2Eieee_2Eflt,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)),V2b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( p(c_2Eieee_2Eflt_2E3(V0X_2E0,V1a_2E0,V2b_2E0))
<=> ( c_2Eieee_2Efcompare_2E3(V0X_2E0,V1a_2E0,V2b_2E0) = c_2Eieee_2ELt_2E0 ) ) ).
tff(thm_2Eieee_2Efle,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)),V2b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( p(c_2Eieee_2Efle_2E3(V0X_2E0,V1a_2E0,V2b_2E0))
<=> ( ( c_2Eieee_2Efcompare_2E3(V0X_2E0,V1a_2E0,V2b_2E0) = c_2Eieee_2ELt_2E0 )
| ( c_2Eieee_2Efcompare_2E3(V0X_2E0,V1a_2E0,V2b_2E0) = c_2Eieee_2EEq_2E0 ) ) ) ).
tff(thm_2Eieee_2Efgt,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)),V2b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( p(c_2Eieee_2Efgt_2E3(V0X_2E0,V1a_2E0,V2b_2E0))
<=> ( c_2Eieee_2Efcompare_2E3(V0X_2E0,V1a_2E0,V2b_2E0) = c_2Eieee_2EGt_2E0 ) ) ).
tff(thm_2Eieee_2Efge,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)),V2b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( p(c_2Eieee_2Efge_2E3(V0X_2E0,V1a_2E0,V2b_2E0))
<=> ( ( c_2Eieee_2Efcompare_2E3(V0X_2E0,V1a_2E0,V2b_2E0) = c_2Eieee_2EGt_2E0 )
| ( c_2Eieee_2Efcompare_2E3(V0X_2E0,V1a_2E0,V2b_2E0) = c_2Eieee_2EEq_2E0 ) ) ) ).
tff(thm_2Eieee_2Efeq,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)),V2b_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( p(c_2Eieee_2Efeq_2E3(V0X_2E0,V1a_2E0,V2b_2E0))
<=> ( c_2Eieee_2Efcompare_2E3(V0X_2E0,V1a_2E0,V2b_2E0) = c_2Eieee_2EEq_2E0 ) ) ).
tff(thm_2Eieee_2Efloat__format,axiom,
c_2Eieee_2Efloat__format_2E0 = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))) ).
tff(thm_2Eieee_2Efloat__TY__DEF,axiom,
? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Eieee_2Efloat,c_2Eieee_2Eis__valid_2E1(c_2Eieee_2Efloat__format_2E0),V0rep_2E0)) ).
tff(thm_2Eieee_2Efloat__tybij,axiom,
( ! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat_2E1(c_2Eieee_2Edefloat_2E1(V0a_2E0)) = V0a_2E0 )
& ! [V1r_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( p(c_2Eieee_2Eis__valid_2E2(c_2Eieee_2Efloat__format_2E0,V1r_2E0))
<=> ( c_2Eieee_2Edefloat_2E1(c_2Eieee_2Efloat_2E1(V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Eieee_2EVal,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EVal_2E1(V0a_2E0) = c_2Eieee_2Evalof_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EFloat,axiom,
! [V0x_2E0: tyop_2Erealax_2Ereal] : ( c_2Eieee_2EFloat_2E1(V0x_2E0) = c_2Eieee_2Efloat_2E1(c_2Eieee_2Eround_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,V0x_2E0)) ) ).
tff(thm_2Eieee_2ESign,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2ESign_2E1(V0a_2E0) = c_2Eieee_2Esign_2E1(c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EExponent,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EExponent_2E1(V0a_2E0) = c_2Eieee_2Eexponent_2E1(c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EFraction,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EFraction_2E1(V0a_2E0) = c_2Eieee_2Efraction_2E1(c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EUlp,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EUlp_2E1(V0a_2E0) = c_2Eieee_2Eulp_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EIsnan,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EIsnan_2E1(V0a_2E0) = c_2Eieee_2Eis__nan_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EInfinity,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EInfinity_2E1(V0a_2E0) = c_2Eieee_2Eis__infinity_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EIsnormal,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EIsnormal_2E1(V0a_2E0) = c_2Eieee_2Eis__normal_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EIsdenormal,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EIsdenormal_2E1(V0a_2E0) = c_2Eieee_2Eis__denormal_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EIszero,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EIszero_2E1(V0a_2E0) = c_2Eieee_2Eis__zero_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EFinite,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] :
( p(c_2Eieee_2EFinite_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_2Eieee_2EIsintegral,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EIsintegral_2E1(V0a_2E0) = c_2Eieee_2Eis__integral_2E2(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2EPlus__zero,axiom,
c_2Eieee_2EPlus__zero_2E0 = c_2Eieee_2Efloat_2E1(c_2Eieee_2Eplus__zero_2E1(c_2Eieee_2Efloat__format_2E0)) ).
tff(thm_2Eieee_2EMinus__zero,axiom,
c_2Eieee_2EMinus__zero_2E0 = c_2Eieee_2Efloat_2E1(c_2Eieee_2Eminus__zero_2E1(c_2Eieee_2Efloat__format_2E0)) ).
tff(thm_2Eieee_2EMinus__infinity,axiom,
c_2Eieee_2EMinus__infinity_2E0 = c_2Eieee_2Efloat_2E1(c_2Eieee_2Eminus__infinity_2E1(c_2Eieee_2Efloat__format_2E0)) ).
tff(thm_2Eieee_2EPlus__infinity,axiom,
c_2Eieee_2EPlus__infinity_2E0 = c_2Eieee_2Efloat_2E1(c_2Eieee_2Eplus__infinity_2E1(c_2Eieee_2Efloat__format_2E0)) ).
tff(thm_2Eieee_2Efloat__add,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__add_2E2(V0a_2E0,V1b_2E0) = c_2Eieee_2Efloat_2E1(c_2Eieee_2Efadd_2E4(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0),c_2Eieee_2Edefloat_2E1(V1b_2E0))) ) ).
tff(thm_2Eieee_2Efloat__sub,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__sub_2E2(V0a_2E0,V1b_2E0) = c_2Eieee_2Efloat_2E1(c_2Eieee_2Efsub_2E4(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0),c_2Eieee_2Edefloat_2E1(V1b_2E0))) ) ).
tff(thm_2Eieee_2Efloat__mul,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__mul_2E2(V0a_2E0,V1b_2E0) = c_2Eieee_2Efloat_2E1(c_2Eieee_2Efmul_2E4(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0),c_2Eieee_2Edefloat_2E1(V1b_2E0))) ) ).
tff(thm_2Eieee_2Efloat__div,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__div_2E2(V0a_2E0,V1b_2E0) = c_2Eieee_2Efloat_2E1(c_2Eieee_2Efdiv_2E4(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0),c_2Eieee_2Edefloat_2E1(V1b_2E0))) ) ).
tff(thm_2Eieee_2Efloat__rem,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__rem_2E2(V0a_2E0,V1b_2E0) = c_2Eieee_2Efloat_2E1(c_2Eieee_2Efrem_2E4(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0),c_2Eieee_2Edefloat_2E1(V1b_2E0))) ) ).
tff(thm_2Eieee_2Efloat__sqrt,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__sqrt_2E1(V0a_2E0) = c_2Eieee_2Efloat_2E1(c_2Eieee_2Efsqrt_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0))) ) ).
tff(thm_2Eieee_2EROUNDFLOAT,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2EROUNDFLOAT_2E1(V0a_2E0) = c_2Eieee_2Efloat_2E1(c_2Eieee_2Efintrnd_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0))) ) ).
tff(thm_2Eieee_2Efloat__lt,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__lt_2E2(V0a_2E0,V1b_2E0) = c_2Eieee_2Eflt_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0),c_2Eieee_2Edefloat_2E1(V1b_2E0)) ) ).
tff(thm_2Eieee_2Efloat__le,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__le_2E2(V0a_2E0,V1b_2E0) = c_2Eieee_2Efle_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0),c_2Eieee_2Edefloat_2E1(V1b_2E0)) ) ).
tff(thm_2Eieee_2Efloat__gt,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__gt_2E2(V0a_2E0,V1b_2E0) = c_2Eieee_2Efgt_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0),c_2Eieee_2Edefloat_2E1(V1b_2E0)) ) ).
tff(thm_2Eieee_2Efloat__ge,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__ge_2E2(V0a_2E0,V1b_2E0) = c_2Eieee_2Efge_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0),c_2Eieee_2Edefloat_2E1(V1b_2E0)) ) ).
tff(thm_2Eieee_2Efloat__eq,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat,V1b_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__eq_2E2(V0a_2E0,V1b_2E0) = c_2Eieee_2Efeq_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0),c_2Eieee_2Edefloat_2E1(V1b_2E0)) ) ).
tff(thm_2Eieee_2Efloat__neg,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__neg_2E1(V0a_2E0) = c_2Eieee_2Efloat_2E1(c_2Eieee_2Efneg_2E3(c_2Eieee_2Efloat__format_2E0,c_2Eieee_2ETo__nearest_2E0,c_2Eieee_2Edefloat_2E1(V0a_2E0))) ) ).
tff(thm_2Eieee_2Efloat__abs,axiom,
! [V0a_2E0: tyop_2Eieee_2Efloat] : ( c_2Eieee_2Efloat__abs_2E1(V0a_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__ge_2E2(V0a_2E0,c_2Eieee_2EPlus__zero_2E0),V0a_2E0,c_2Eieee_2Efloat__neg_2E1(V0a_2E0)) ) ).
tff(thm_2Eieee_2Enum2roundmode__roundmode2num,axiom,
! [V0a_2E0: tyop_2Eieee_2Eroundmode] : ( c_2Eieee_2Enum2roundmode_2E1(c_2Eieee_2Eroundmode2num_2E1(V0a_2E0)) = V0a_2E0 ) ).
tff(thm_2Eieee_2Eroundmode2num__num2roundmode,axiom,
! [V0r_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0r_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
<=> ( c_2Eieee_2Eroundmode2num_2E1(c_2Eieee_2Enum2roundmode_2E1(V0r_2E0)) = V0r_2E0 ) ) ).
tff(thm_2Eieee_2Enum2roundmode__11,axiom,
! [V0r_2E0: tyop_2Enum_2Enum,V1r_27_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0r_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
=> ( p(c_2Eprim__rec_2E_3C_2E2(V1r_27_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
=> ( ( c_2Eieee_2Enum2roundmode_2E1(V0r_2E0) = c_2Eieee_2Enum2roundmode_2E1(V1r_27_2E0) )
<=> ( V0r_2E0 = V1r_27_2E0 ) ) ) ) ).
tff(thm_2Eieee_2Eroundmode2num__11,axiom,
! [V0a_2E0: tyop_2Eieee_2Eroundmode,V1a_27_2E0: tyop_2Eieee_2Eroundmode] :
( ( c_2Eieee_2Eroundmode2num_2E1(V0a_2E0) = c_2Eieee_2Eroundmode2num_2E1(V1a_27_2E0) )
<=> ( V0a_2E0 = V1a_27_2E0 ) ) ).
tff(thm_2Eieee_2Enum2roundmode__ONTO,axiom,
! [V0a_2E0: tyop_2Eieee_2Eroundmode] :
? [V1r_2E0: tyop_2Enum_2Enum] :
( ( V0a_2E0 = c_2Eieee_2Enum2roundmode_2E1(V1r_2E0) )
& p(c_2Eprim__rec_2E_3C_2E2(V1r_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).
tff(thm_2Eieee_2Eroundmode2num__ONTO,axiom,
! [V0r_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0r_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
<=> ? [V1a_2E0: tyop_2Eieee_2Eroundmode] : ( V0r_2E0 = c_2Eieee_2Eroundmode2num_2E1(V1a_2E0) ) ) ).
tff(thm_2Eieee_2Enum2roundmode__thm,axiom,
( ( c_2Eieee_2Enum2roundmode_2E1(c_2Enum_2E0_2E0) = c_2Eieee_2ETo__nearest_2E0 )
& ( c_2Eieee_2Enum2roundmode_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Eieee_2Efloat__To__zero_2E0 )
& ( c_2Eieee_2Enum2roundmode_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Eieee_2ETo__pinfinity_2E0 )
& ( c_2Eieee_2Enum2roundmode_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Eieee_2ETo__ninfinity_2E0 ) ) ).
tff(thm_2Eieee_2Eroundmode2num__thm,axiom,
( ( c_2Eieee_2Eroundmode2num_2E1(c_2Eieee_2ETo__nearest_2E0) = c_2Enum_2E0_2E0 )
& ( c_2Eieee_2Eroundmode2num_2E1(c_2Eieee_2Efloat__To__zero_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ( c_2Eieee_2Eroundmode2num_2E1(c_2Eieee_2ETo__pinfinity_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ( c_2Eieee_2Eroundmode2num_2E1(c_2Eieee_2ETo__ninfinity_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Eieee_2Eroundmode__EQ__roundmode,axiom,
! [V0a_2E0: tyop_2Eieee_2Eroundmode,V1a_27_2E0: tyop_2Eieee_2Eroundmode] :
( ( V0a_2E0 = V1a_27_2E0 )
<=> ( c_2Eieee_2Eroundmode2num_2E1(V0a_2E0) = c_2Eieee_2Eroundmode2num_2E1(V1a_27_2E0) ) ) ).
tff(thm_2Eieee_2Eroundmode__case__def,axiom,
! [A_27a: $tType] :
( ! [V0v0_2E0: A_27a,V1v1_2E0: A_27a,V2v2_2E0: A_27a,V3v3_2E0: A_27a] : ( c_2Eieee_2Eroundmode__CASE_2E5(A_27a,c_2Eieee_2ETo__nearest_2E0,V0v0_2E0,V1v1_2E0,V2v2_2E0,V3v3_2E0) = V0v0_2E0 )
& ! [V4v0_2E0: A_27a,V5v1_2E0: A_27a,V6v2_2E0: A_27a,V7v3_2E0: A_27a] : ( c_2Eieee_2Eroundmode__CASE_2E5(A_27a,c_2Eieee_2Efloat__To__zero_2E0,V4v0_2E0,V5v1_2E0,V6v2_2E0,V7v3_2E0) = V5v1_2E0 )
& ! [V8v0_2E0: A_27a,V9v1_2E0: A_27a,V10v2_2E0: A_27a,V11v3_2E0: A_27a] : ( c_2Eieee_2Eroundmode__CASE_2E5(A_27a,c_2Eieee_2ETo__pinfinity_2E0,V8v0_2E0,V9v1_2E0,V10v2_2E0,V11v3_2E0) = V10v2_2E0 )
& ! [V12v0_2E0: A_27a,V13v1_2E0: A_27a,V14v2_2E0: A_27a,V15v3_2E0: A_27a] : ( c_2Eieee_2Eroundmode__CASE_2E5(A_27a,c_2Eieee_2ETo__ninfinity_2E0,V12v0_2E0,V13v1_2E0,V14v2_2E0,V15v3_2E0) = V15v3_2E0 ) ) ).
tff(thm_2Eieee_2Edatatype__roundmode,axiom,
! [V0roundmode_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool))))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool),app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool))),V0roundmode_2E0,c_2Eieee_2ETo__nearest_2E0),c_2Eieee_2Efloat__To__zero_2E0),c_2Eieee_2ETo__pinfinity_2E0),c_2Eieee_2ETo__ninfinity_2E0))) ).
tff(thm_2Eieee_2Eroundmode__distinct,axiom,
( ( c_2Eieee_2ETo__nearest_2E0 != c_2Eieee_2Efloat__To__zero_2E0 )
& ( c_2Eieee_2ETo__nearest_2E0 != c_2Eieee_2ETo__pinfinity_2E0 )
& ( c_2Eieee_2ETo__nearest_2E0 != c_2Eieee_2ETo__ninfinity_2E0 )
& ( c_2Eieee_2Efloat__To__zero_2E0 != c_2Eieee_2ETo__pinfinity_2E0 )
& ( c_2Eieee_2Efloat__To__zero_2E0 != c_2Eieee_2ETo__ninfinity_2E0 )
& ( c_2Eieee_2ETo__pinfinity_2E0 != c_2Eieee_2ETo__ninfinity_2E0 ) ) ).
tff(thm_2Eieee_2Eroundmode__nchotomy,axiom,
! [V0a_2E0: tyop_2Eieee_2Eroundmode] :
( ( V0a_2E0 = c_2Eieee_2ETo__nearest_2E0 )
| ( V0a_2E0 = c_2Eieee_2Efloat__To__zero_2E0 )
| ( V0a_2E0 = c_2Eieee_2ETo__pinfinity_2E0 )
| ( V0a_2E0 = c_2Eieee_2ETo__ninfinity_2E0 ) ) ).
tff(thm_2Eieee_2Eroundmode__Axiom,axiom,
! [A_27a: $tType,V0x0_2E0: A_27a,V1x1_2E0: A_27a,V2x2_2E0: A_27a,V3x3_2E0: A_27a] :
? [V4f_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,A_27a)] :
( ( app_2E2(tyop_2Eieee_2Eroundmode,A_27a,V4f_2E0,c_2Eieee_2ETo__nearest_2E0) = V0x0_2E0 )
& ( app_2E2(tyop_2Eieee_2Eroundmode,A_27a,V4f_2E0,c_2Eieee_2Efloat__To__zero_2E0) = V1x1_2E0 )
& ( app_2E2(tyop_2Eieee_2Eroundmode,A_27a,V4f_2E0,c_2Eieee_2ETo__pinfinity_2E0) = V2x2_2E0 )
& ( app_2E2(tyop_2Eieee_2Eroundmode,A_27a,V4f_2E0,c_2Eieee_2ETo__ninfinity_2E0) = V3x3_2E0 ) ) ).
tff(thm_2Eieee_2Eroundmode__induction,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,V0P_2E0,c_2Eieee_2ETo__nearest_2E0))
& p(app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,V0P_2E0,c_2Eieee_2ETo__ninfinity_2E0))
& p(app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,V0P_2E0,c_2Eieee_2ETo__pinfinity_2E0))
& p(app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,V0P_2E0,c_2Eieee_2Efloat__To__zero_2E0)) )
=> ! [V1a_2E0: tyop_2Eieee_2Eroundmode] : p(app_2E2(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Ebool,V0P_2E0,V1a_2E0)) ) ).
tff(thm_2Eieee_2Eroundmode__case__cong,axiom,
! [A_27a: $tType,V0v3_27_2E0: A_27a,V1v2_27_2E0: A_27a,V2v1_27_2E0: A_27a,V3v0_27_2E0: A_27a,V4M_2E0: tyop_2Eieee_2Eroundmode,V5M_27_2E0: tyop_2Eieee_2Eroundmode,V6v0_2E0: A_27a,V7v1_2E0: A_27a,V8v2_2E0: A_27a,V9v3_2E0: A_27a] :
( ( ( V4M_2E0 = V5M_27_2E0 )
& ( ( V5M_27_2E0 = c_2Eieee_2ETo__nearest_2E0 )
=> ( V6v0_2E0 = V3v0_27_2E0 ) )
& ( ( V5M_27_2E0 = c_2Eieee_2Efloat__To__zero_2E0 )
=> ( V7v1_2E0 = V2v1_27_2E0 ) )
& ( ( V5M_27_2E0 = c_2Eieee_2ETo__pinfinity_2E0 )
=> ( V8v2_2E0 = V1v2_27_2E0 ) )
& ( ( V5M_27_2E0 = c_2Eieee_2ETo__ninfinity_2E0 )
=> ( V9v3_2E0 = V0v3_27_2E0 ) ) )
=> ( c_2Eieee_2Eroundmode__CASE_2E5(A_27a,V4M_2E0,V6v0_2E0,V7v1_2E0,V8v2_2E0,V9v3_2E0) = c_2Eieee_2Eroundmode__CASE_2E5(A_27a,V5M_27_2E0,V3v0_27_2E0,V2v1_27_2E0,V1v2_27_2E0,V0v3_27_2E0) ) ) ).
tff(thm_2Eieee_2Eroundmode__case__eq,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eieee_2Eroundmode,V1v3_2E0: A_27a,V2v2_2E0: A_27a,V3v1_2E0: A_27a,V4v0_2E0: A_27a,V5v_2E0: A_27a] :
( ( c_2Eieee_2Eroundmode__CASE_2E5(A_27a,V0x_2E0,V4v0_2E0,V3v1_2E0,V2v2_2E0,V1v3_2E0) = V5v_2E0 )
<=> ( ( ( V0x_2E0 = c_2Eieee_2ETo__nearest_2E0 )
& ( V4v0_2E0 = V5v_2E0 ) )
| ( ( V0x_2E0 = c_2Eieee_2Efloat__To__zero_2E0 )
& ( V3v1_2E0 = V5v_2E0 ) )
| ( ( V0x_2E0 = c_2Eieee_2ETo__pinfinity_2E0 )
& ( V2v2_2E0 = V5v_2E0 ) )
| ( ( V0x_2E0 = c_2Eieee_2ETo__ninfinity_2E0 )
& ( V1v3_2E0 = V5v_2E0 ) ) ) ) ).
tff(thm_2Eieee_2Enum2ccode__ccode2num,axiom,
! [V0a_2E0: tyop_2Eieee_2Eccode] : ( c_2Eieee_2Enum2ccode_2E1(c_2Eieee_2Eccode2num_2E1(V0a_2E0)) = V0a_2E0 ) ).
tff(thm_2Eieee_2Eccode2num__num2ccode,axiom,
! [V0r_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0r_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
<=> ( c_2Eieee_2Eccode2num_2E1(c_2Eieee_2Enum2ccode_2E1(V0r_2E0)) = V0r_2E0 ) ) ).
tff(thm_2Eieee_2Enum2ccode__11,axiom,
! [V0r_2E0: tyop_2Enum_2Enum,V1r_27_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0r_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
=> ( p(c_2Eprim__rec_2E_3C_2E2(V1r_27_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
=> ( ( c_2Eieee_2Enum2ccode_2E1(V0r_2E0) = c_2Eieee_2Enum2ccode_2E1(V1r_27_2E0) )
<=> ( V0r_2E0 = V1r_27_2E0 ) ) ) ) ).
tff(thm_2Eieee_2Eccode2num__11,axiom,
! [V0a_2E0: tyop_2Eieee_2Eccode,V1a_27_2E0: tyop_2Eieee_2Eccode] :
( ( c_2Eieee_2Eccode2num_2E1(V0a_2E0) = c_2Eieee_2Eccode2num_2E1(V1a_27_2E0) )
<=> ( V0a_2E0 = V1a_27_2E0 ) ) ).
tff(thm_2Eieee_2Enum2ccode__ONTO,axiom,
! [V0a_2E0: tyop_2Eieee_2Eccode] :
? [V1r_2E0: tyop_2Enum_2Enum] :
( ( V0a_2E0 = c_2Eieee_2Enum2ccode_2E1(V1r_2E0) )
& p(c_2Eprim__rec_2E_3C_2E2(V1r_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).
tff(thm_2Eieee_2Eccode2num__ONTO,axiom,
! [V0r_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0r_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
<=> ? [V1a_2E0: tyop_2Eieee_2Eccode] : ( V0r_2E0 = c_2Eieee_2Eccode2num_2E1(V1a_2E0) ) ) ).
tff(thm_2Eieee_2Enum2ccode__thm,axiom,
( ( c_2Eieee_2Enum2ccode_2E1(c_2Enum_2E0_2E0) = c_2Eieee_2EGt_2E0 )
& ( c_2Eieee_2Enum2ccode_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Eieee_2ELt_2E0 )
& ( c_2Eieee_2Enum2ccode_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) = c_2Eieee_2EEq_2E0 )
& ( c_2Eieee_2Enum2ccode_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Eieee_2EUn_2E0 ) ) ).
tff(thm_2Eieee_2Eccode2num__thm,axiom,
( ( c_2Eieee_2Eccode2num_2E1(c_2Eieee_2EGt_2E0) = c_2Enum_2E0_2E0 )
& ( c_2Eieee_2Eccode2num_2E1(c_2Eieee_2ELt_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ( c_2Eieee_2Eccode2num_2E1(c_2Eieee_2EEq_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ( c_2Eieee_2Eccode2num_2E1(c_2Eieee_2EUn_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Eieee_2Eccode__EQ__ccode,axiom,
! [V0a_2E0: tyop_2Eieee_2Eccode,V1a_27_2E0: tyop_2Eieee_2Eccode] :
( ( V0a_2E0 = V1a_27_2E0 )
<=> ( c_2Eieee_2Eccode2num_2E1(V0a_2E0) = c_2Eieee_2Eccode2num_2E1(V1a_27_2E0) ) ) ).
tff(thm_2Eieee_2Eccode__case__def,axiom,
! [A_27a: $tType] :
( ! [V0v0_2E0: A_27a,V1v1_2E0: A_27a,V2v2_2E0: A_27a,V3v3_2E0: A_27a] : ( c_2Eieee_2Eccode__CASE_2E5(A_27a,c_2Eieee_2EGt_2E0,V0v0_2E0,V1v1_2E0,V2v2_2E0,V3v3_2E0) = V0v0_2E0 )
& ! [V4v0_2E0: A_27a,V5v1_2E0: A_27a,V6v2_2E0: A_27a,V7v3_2E0: A_27a] : ( c_2Eieee_2Eccode__CASE_2E5(A_27a,c_2Eieee_2ELt_2E0,V4v0_2E0,V5v1_2E0,V6v2_2E0,V7v3_2E0) = V5v1_2E0 )
& ! [V8v0_2E0: A_27a,V9v1_2E0: A_27a,V10v2_2E0: A_27a,V11v3_2E0: A_27a] : ( c_2Eieee_2Eccode__CASE_2E5(A_27a,c_2Eieee_2EEq_2E0,V8v0_2E0,V9v1_2E0,V10v2_2E0,V11v3_2E0) = V10v2_2E0 )
& ! [V12v0_2E0: A_27a,V13v1_2E0: A_27a,V14v2_2E0: A_27a,V15v3_2E0: A_27a] : ( c_2Eieee_2Eccode__CASE_2E5(A_27a,c_2Eieee_2EUn_2E0,V12v0_2E0,V13v1_2E0,V14v2_2E0,V15v3_2E0) = V15v3_2E0 ) ) ).
tff(thm_2Eieee_2Edatatype__ccode,axiom,
! [V0ccode_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool))))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool,app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool),app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool))),V0ccode_2E0,c_2Eieee_2EGt_2E0),c_2Eieee_2ELt_2E0),c_2Eieee_2EEq_2E0),c_2Eieee_2EUn_2E0))) ).
tff(thm_2Eieee_2Eccode__distinct,axiom,
( ( c_2Eieee_2EGt_2E0 != c_2Eieee_2ELt_2E0 )
& ( c_2Eieee_2EGt_2E0 != c_2Eieee_2EEq_2E0 )
& ( c_2Eieee_2EGt_2E0 != c_2Eieee_2EUn_2E0 )
& ( c_2Eieee_2ELt_2E0 != c_2Eieee_2EEq_2E0 )
& ( c_2Eieee_2ELt_2E0 != c_2Eieee_2EUn_2E0 )
& ( c_2Eieee_2EEq_2E0 != c_2Eieee_2EUn_2E0 ) ) ).
tff(thm_2Eieee_2Eccode__nchotomy,axiom,
! [V0a_2E0: tyop_2Eieee_2Eccode] :
( ( V0a_2E0 = c_2Eieee_2EGt_2E0 )
| ( V0a_2E0 = c_2Eieee_2ELt_2E0 )
| ( V0a_2E0 = c_2Eieee_2EEq_2E0 )
| ( V0a_2E0 = c_2Eieee_2EUn_2E0 ) ) ).
tff(thm_2Eieee_2Eccode__Axiom,axiom,
! [A_27a: $tType,V0x0_2E0: A_27a,V1x1_2E0: A_27a,V2x2_2E0: A_27a,V3x3_2E0: A_27a] :
? [V4f_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,A_27a)] :
( ( app_2E2(tyop_2Eieee_2Eccode,A_27a,V4f_2E0,c_2Eieee_2EGt_2E0) = V0x0_2E0 )
& ( app_2E2(tyop_2Eieee_2Eccode,A_27a,V4f_2E0,c_2Eieee_2ELt_2E0) = V1x1_2E0 )
& ( app_2E2(tyop_2Eieee_2Eccode,A_27a,V4f_2E0,c_2Eieee_2EEq_2E0) = V2x2_2E0 )
& ( app_2E2(tyop_2Eieee_2Eccode,A_27a,V4f_2E0,c_2Eieee_2EUn_2E0) = V3x3_2E0 ) ) ).
tff(thm_2Eieee_2Eccode__induction,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool,V0P_2E0,c_2Eieee_2EEq_2E0))
& p(app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool,V0P_2E0,c_2Eieee_2EGt_2E0))
& p(app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool,V0P_2E0,c_2Eieee_2ELt_2E0))
& p(app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool,V0P_2E0,c_2Eieee_2EUn_2E0)) )
=> ! [V1a_2E0: tyop_2Eieee_2Eccode] : p(app_2E2(tyop_2Eieee_2Eccode,tyop_2Emin_2Ebool,V0P_2E0,V1a_2E0)) ) ).
tff(thm_2Eieee_2Eccode__case__cong,axiom,
! [A_27a: $tType,V0v3_27_2E0: A_27a,V1v2_27_2E0: A_27a,V2v1_27_2E0: A_27a,V3v0_27_2E0: A_27a,V4M_2E0: tyop_2Eieee_2Eccode,V5M_27_2E0: tyop_2Eieee_2Eccode,V6v0_2E0: A_27a,V7v1_2E0: A_27a,V8v2_2E0: A_27a,V9v3_2E0: A_27a] :
( ( ( V4M_2E0 = V5M_27_2E0 )
& ( ( V5M_27_2E0 = c_2Eieee_2EGt_2E0 )
=> ( V6v0_2E0 = V3v0_27_2E0 ) )
& ( ( V5M_27_2E0 = c_2Eieee_2ELt_2E0 )
=> ( V7v1_2E0 = V2v1_27_2E0 ) )
& ( ( V5M_27_2E0 = c_2Eieee_2EEq_2E0 )
=> ( V8v2_2E0 = V1v2_27_2E0 ) )
& ( ( V5M_27_2E0 = c_2Eieee_2EUn_2E0 )
=> ( V9v3_2E0 = V0v3_27_2E0 ) ) )
=> ( c_2Eieee_2Eccode__CASE_2E5(A_27a,V4M_2E0,V6v0_2E0,V7v1_2E0,V8v2_2E0,V9v3_2E0) = c_2Eieee_2Eccode__CASE_2E5(A_27a,V5M_27_2E0,V3v0_27_2E0,V2v1_27_2E0,V1v2_27_2E0,V0v3_27_2E0) ) ) ).
tff(thm_2Eieee_2Eccode__case__eq,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eieee_2Eccode,V1v3_2E0: A_27a,V2v2_2E0: A_27a,V3v1_2E0: A_27a,V4v0_2E0: A_27a,V5v_2E0: A_27a] :
( ( c_2Eieee_2Eccode__CASE_2E5(A_27a,V0x_2E0,V4v0_2E0,V3v1_2E0,V2v2_2E0,V1v3_2E0) = V5v_2E0 )
<=> ( ( ( V0x_2E0 = c_2Eieee_2EGt_2E0 )
& ( V4v0_2E0 = V5v_2E0 ) )
| ( ( V0x_2E0 = c_2Eieee_2ELt_2E0 )
& ( V3v1_2E0 = V5v_2E0 ) )
| ( ( V0x_2E0 = c_2Eieee_2EEq_2E0 )
& ( V2v2_2E0 = V5v_2E0 ) )
| ( ( V0x_2E0 = c_2Eieee_2EUn_2E0 )
& ( V1v3_2E0 = V5v_2E0 ) ) ) ) ).
%------------------------------------------------------------------------------