ITP001 Axioms: ITP140^4.ax
%------------------------------------------------------------------------------
% File : ITP140^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : lift_ieee.ax [Gau19]
% : HL4140^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 401 ( 116 unt; 234 typ; 0 def)
% Number of atoms : 380 ( 152 equ; 14 cnn)
% Maximal formula atoms : 8 ( 0 avg)
% Number of connectives : 7104 ( 14 ~; 1 |; 88 &;6940 @)
% ( 11 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg;6940 nst)
% Number of types : 8 ( 7 usr)
% Number of type conns : 345 ( 345 >; 0 *; 0 +; 0 <<)
% Number of symbols : 229 ( 227 usr; 85 con; 0-4 aty)
% Number of variables : 482 ( 0 ^ 471 !; 11 ?; 482 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
u: $tType ).
thf(d,type,
d: $tType ).
thf(du,type,
du: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2Erealax_2Ereal,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
thf(mono_2Etyop_2Ebinary__ieee_2Erounding,type,
mono_2Etyop_2Ebinary__ieee_2Erounding: $tType ).
thf(tyop_2Ebinary__ieee_2Eflags,type,
tyop_2Ebinary__ieee_2Eflags: d ).
thf(tyop_2Ebinary__ieee_2Efloat,type,
tyop_2Ebinary__ieee_2Efloat: d > d > d ).
thf(tyop_2Ebinary__ieee_2Erounding,type,
tyop_2Ebinary__ieee_2Erounding: d ).
thf(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: d > d ).
thf(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: d > d > d ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: d > d > d ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: d ).
thf(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: d ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: d ).
thf(s,type,
s: d > u > du ).
thf(app_2E2,type,
app_2E2: du > du > u ).
thf(combin_i_2E0,type,
combin_i_2E0: u ).
thf(combin_k_2E0,type,
combin_k_2E0: u ).
thf(combin_s_2E0,type,
combin_s_2E0: u ).
thf(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: u ).
thf(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: u ).
thf(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: du > du > u ).
thf(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0: u ).
thf(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2: du > du > u ).
thf(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: u ).
thf(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: du > du > u ).
thf(c_2Ereal_2E_2F_2E0,type,
c_2Ereal_2E_2F_2E0: u ).
thf(c_2Ereal_2E_2F_2E2,type,
c_2Ereal_2E_2F_2E2: du > du > u ).
thf(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: du > du > u ).
thf(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: u ).
thf(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: du > u ).
thf(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: u ).
thf(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: du > u ).
thf(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0: u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0: u ).
thf(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1: du > u ).
thf(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0: u ).
thf(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1: du > u ).
thf(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0: u ).
thf(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2: du > du > u ).
thf(c_2Ewords_2EINT__MAX_2E0,type,
c_2Ewords_2EINT__MAX_2E0: u ).
thf(c_2Ewords_2EINT__MAX_2E1,type,
c_2Ewords_2EINT__MAX_2E1: du > u ).
thf(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: u ).
thf(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: du > u ).
thf(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0: u ).
thf(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1: du > u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0: u ).
thf(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(c_2Ereal_2Eabs_2E0,type,
c_2Ereal_2Eabs_2E0: u ).
thf(c_2Ereal_2Eabs_2E1,type,
c_2Ereal_2Eabs_2E1: du > u ).
thf(c_2Ebinary__ieee_2Eclosest__such_2E0,type,
c_2Ebinary__ieee_2Eclosest__such_2E0: u ).
thf(c_2Ebinary__ieee_2Eclosest__such_2E3,type,
c_2Ebinary__ieee_2Eclosest__such_2E3: du > du > du > u ).
thf(c_2Efcp_2Edimindex_2E0,type,
c_2Efcp_2Edimindex_2E0: u ).
thf(c_2Efcp_2Edimindex_2E1,type,
c_2Efcp_2Edimindex_2E1: du > u ).
thf(c_2Elift__ieee_2Eerror_2E0,type,
c_2Elift__ieee_2Eerror_2E0: u ).
thf(c_2Elift__ieee_2Eerror_2E2,type,
c_2Elift__ieee_2Eerror_2E2: du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__Sign_2E0,type,
c_2Ebinary__ieee_2Efloat__Sign_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__Sign_2E1,type,
c_2Ebinary__ieee_2Efloat__Sign_2E1: du > u ).
thf(c_2Ebinary__ieee_2Efloat__add_2E0,type,
c_2Ebinary__ieee_2Efloat__add_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__add_2E3,type,
c_2Ebinary__ieee_2Efloat__add_2E3: du > du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__div_2E0,type,
c_2Ebinary__ieee_2Efloat__div_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__div_2E3,type,
c_2Ebinary__ieee_2Efloat__div_2E3: du > du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__equal_2E0,type,
c_2Ebinary__ieee_2Efloat__equal_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__equal_2E2,type,
c_2Ebinary__ieee_2Efloat__equal_2E2: du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__greater__equal_2E0,type,
c_2Ebinary__ieee_2Efloat__greater__equal_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__greater__equal_2E2,type,
c_2Ebinary__ieee_2Efloat__greater__equal_2E2: du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__greater__than_2E0,type,
c_2Ebinary__ieee_2Efloat__greater__than_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__greater__than_2E2,type,
c_2Ebinary__ieee_2Efloat__greater__than_2E2: du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__is__finite_2E0,type,
c_2Ebinary__ieee_2Efloat__is__finite_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__is__finite_2E1,type,
c_2Ebinary__ieee_2Efloat__is__finite_2E1: du > u ).
thf(c_2Ebinary__ieee_2Efloat__is__nan_2E0,type,
c_2Ebinary__ieee_2Efloat__is__nan_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__is__nan_2E1,type,
c_2Ebinary__ieee_2Efloat__is__nan_2E1: du > u ).
thf(c_2Ebinary__ieee_2Efloat__is__zero_2E0,type,
c_2Ebinary__ieee_2Efloat__is__zero_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__is__zero_2E1,type,
c_2Ebinary__ieee_2Efloat__is__zero_2E1: du > u ).
thf(c_2Ebinary__ieee_2Efloat__less__equal_2E0,type,
c_2Ebinary__ieee_2Efloat__less__equal_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__less__equal_2E2,type,
c_2Ebinary__ieee_2Efloat__less__equal_2E2: du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__less__than_2E0,type,
c_2Ebinary__ieee_2Efloat__less__than_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__less__than_2E2,type,
c_2Ebinary__ieee_2Efloat__less__than_2E2: du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__mul_2E0,type,
c_2Ebinary__ieee_2Efloat__mul_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__mul_2E3,type,
c_2Ebinary__ieee_2Efloat__mul_2E3: du > du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__mul__add_2E0,type,
c_2Ebinary__ieee_2Efloat__mul__add_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__mul__add_2E4,type,
c_2Ebinary__ieee_2Efloat__mul__add_2E4: du > du > du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__mul__sub_2E0,type,
c_2Ebinary__ieee_2Efloat__mul__sub_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__mul__sub_2E4,type,
c_2Ebinary__ieee_2Efloat__mul__sub_2E4: du > du > du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__round_2E0,type,
c_2Ebinary__ieee_2Efloat__round_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__round_2E3,type,
c_2Ebinary__ieee_2Efloat__round_2E3: du > du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__sqrt_2E0,type,
c_2Ebinary__ieee_2Efloat__sqrt_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__sqrt_2E2,type,
c_2Ebinary__ieee_2Efloat__sqrt_2E2: du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__sub_2E0,type,
c_2Ebinary__ieee_2Efloat__sub_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__sub_2E3,type,
c_2Ebinary__ieee_2Efloat__sub_2E3: du > du > du > u ).
thf(c_2Ebinary__ieee_2Efloat__to__real_2E0,type,
c_2Ebinary__ieee_2Efloat__to__real_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__to__real_2E1,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1: du > u ).
thf(c_2Erealax_2Einv_2E0,type,
c_2Erealax_2Einv_2E0: u ).
thf(c_2Erealax_2Einv_2E1,type,
c_2Erealax_2Einv_2E1: du > u ).
thf(c_2Ebinary__ieee_2Eis__closest_2E0,type,
c_2Ebinary__ieee_2Eis__closest_2E0: u ).
thf(c_2Ebinary__ieee_2Eis__closest_2E3,type,
c_2Ebinary__ieee_2Eis__closest_2E3: du > du > du > u ).
thf(c_2Ebinary__ieee_2Elargest_2E0,type,
c_2Ebinary__ieee_2Elargest_2E0: u ).
thf(c_2Ebinary__ieee_2Elargest_2E1,type,
c_2Ebinary__ieee_2Elargest_2E1: du > u ).
thf(c_2Ewords_2En2w_2E0,type,
c_2Ewords_2En2w_2E0: u ).
thf(c_2Ewords_2En2w_2E1,type,
c_2Ewords_2En2w_2E1: du > u ).
thf(c_2Elift__ieee_2Enormalizes_2E0,type,
c_2Elift__ieee_2Enormalizes_2E0: u ).
thf(c_2Elift__ieee_2Enormalizes_2E2,type,
c_2Elift__ieee_2Enormalizes_2E2: du > du > u ).
thf(c_2Ereal_2Epow_2E0,type,
c_2Ereal_2Epow_2E0: u ).
thf(c_2Ereal_2Epow_2E2,type,
c_2Ereal_2Epow_2E2: du > du > u ).
thf(c_2Erealax_2Ereal__add_2E0,type,
c_2Erealax_2Ereal__add_2E0: u ).
thf(c_2Erealax_2Ereal__add_2E2,type,
c_2Erealax_2Ereal__add_2E2: du > du > u ).
thf(c_2Ereal_2Ereal__ge_2E0,type,
c_2Ereal_2Ereal__ge_2E0: u ).
thf(c_2Ereal_2Ereal__ge_2E2,type,
c_2Ereal_2Ereal__ge_2E2: du > du > u ).
thf(c_2Ereal_2Ereal__gt_2E0,type,
c_2Ereal_2Ereal__gt_2E0: u ).
thf(c_2Ereal_2Ereal__gt_2E2,type,
c_2Ereal_2Ereal__gt_2E2: du > du > u ).
thf(c_2Erealax_2Ereal__lt_2E0,type,
c_2Erealax_2Ereal__lt_2E0: u ).
thf(c_2Erealax_2Ereal__lt_2E2,type,
c_2Erealax_2Ereal__lt_2E2: du > du > u ).
thf(c_2Ereal_2Ereal__lte_2E0,type,
c_2Ereal_2Ereal__lte_2E0: u ).
thf(c_2Ereal_2Ereal__lte_2E2,type,
c_2Ereal_2Ereal__lte_2E2: du > du > u ).
thf(c_2Erealax_2Ereal__mul_2E0,type,
c_2Erealax_2Ereal__mul_2E0: u ).
thf(c_2Erealax_2Ereal__mul_2E2,type,
c_2Erealax_2Ereal__mul_2E2: du > du > u ).
thf(c_2Erealax_2Ereal__neg_2E0,type,
c_2Erealax_2Ereal__neg_2E0: u ).
thf(c_2Erealax_2Ereal__neg_2E1,type,
c_2Erealax_2Ereal__neg_2E1: du > u ).
thf(c_2Ereal_2Ereal__of__num_2E0,type,
c_2Ereal_2Ereal__of__num_2E0: u ).
thf(c_2Ereal_2Ereal__of__num_2E1,type,
c_2Ereal_2Ereal__of__num_2E1: du > u ).
thf(c_2Ereal_2Ereal__sub_2E0,type,
c_2Ereal_2Ereal__sub_2E0: u ).
thf(c_2Ereal_2Ereal__sub_2E2,type,
c_2Ereal_2Ereal__sub_2E2: du > du > u ).
thf(c_2Ebinary__ieee_2Ereal__to__float_2E0,type,
c_2Ebinary__ieee_2Ereal__to__float_2E0: u ).
thf(c_2Ebinary__ieee_2Ereal__to__float_2E2,type,
c_2Ebinary__ieee_2Ereal__to__float_2E2: du > du > u ).
thf(c_2Ebinary__ieee_2Eround_2E0,type,
c_2Ebinary__ieee_2Eround_2E0: u ).
thf(c_2Ebinary__ieee_2Eround_2E2,type,
c_2Ebinary__ieee_2Eround_2E2: du > du > u ).
thf(c_2Ebinary__ieee_2EroundTiesToEven_2E0,type,
c_2Ebinary__ieee_2EroundTiesToEven_2E0: u ).
thf(c_2Etransc_2Esqrt_2E0,type,
c_2Etransc_2Esqrt_2E0: u ).
thf(c_2Etransc_2Esqrt_2E1,type,
c_2Etransc_2Esqrt_2E1: du > u ).
thf(c_2Ebool_2Ethe__value_2E0,type,
c_2Ebool_2Ethe__value_2E0: u ).
thf(c_2Ebinary__ieee_2Ethreshold_2E0,type,
c_2Ebinary__ieee_2Ethreshold_2E0: u ).
thf(c_2Ebinary__ieee_2Ethreshold_2E1,type,
c_2Ebinary__ieee_2Ethreshold_2E1: du > u ).
thf(c_2Ebinary__ieee_2Eulp_2E0,type,
c_2Ebinary__ieee_2Eulp_2E0: u ).
thf(c_2Ebinary__ieee_2Eulp_2E1,type,
c_2Ebinary__ieee_2Eulp_2E1: du > u ).
thf(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: u ).
thf(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Earithmetic_2E_2B,type,
mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2D,type,
mono_2Ec_2Earithmetic_2E_2D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ereal_2E_2F,type,
mono_2Ec_2Ereal_2E_2F: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Enum_2E0,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Eprim__rec_2E_3C,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Earithmetic_2EBIT1,type,
mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EBIT2,type,
mono_2Ec_2Earithmetic_2EBIT2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Earithmetic_2EZERO,type,
mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_5C_2F,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(mono_2Ec_2Ereal_2Eabs,type,
mono_2Ec_2Ereal_2Eabs: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Erealax_2Einv,type,
mono_2Ec_2Erealax_2Einv: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ewords_2En2w_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Ewords_2En2w_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Ereal_2Epow,type,
mono_2Ec_2Ereal_2Epow: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Erealax_2Ereal__add,type,
mono_2Ec_2Erealax_2Ereal__add: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ereal_2Ereal__ge,type,
mono_2Ec_2Ereal_2Ereal__ge: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Ereal_2Ereal__gt,type,
mono_2Ec_2Ereal_2Ereal__gt: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Erealax_2Ereal__lt,type,
mono_2Ec_2Erealax_2Ereal__lt: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Ereal_2Ereal__lte,type,
mono_2Ec_2Ereal_2Ereal__lte: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Erealax_2Ereal__mul,type,
mono_2Ec_2Erealax_2Ereal__mul: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Erealax_2Ereal__neg,type,
mono_2Ec_2Erealax_2Ereal__neg: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ereal_2Ereal__of__num,type,
mono_2Ec_2Ereal_2Ereal__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ereal_2Ereal__sub,type,
mono_2Ec_2Ereal_2Ereal__sub: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ebinary__ieee_2EroundTiesToEven,type,
mono_2Ec_2Ebinary__ieee_2EroundTiesToEven: mono_2Etyop_2Ebinary__ieee_2Erounding ).
thf(mono_2Ec_2Etransc_2Esqrt,type,
mono_2Ec_2Etransc_2Esqrt: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ebool_2E_7E,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(i_mono_2Etyop_2Emin_2Ebool,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(i_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,type,
i_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29: mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).
thf(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(i_mono_2Etyop_2Erealax_2Ereal,type,
i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
thf(i_mono_2Etyop_2Ebinary__ieee_2Erounding,type,
i_mono_2Etyop_2Ebinary__ieee_2Erounding: mono_2Etyop_2Ebinary__ieee_2Erounding > u ).
thf(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(j_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,type,
j_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29: du > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Erealax_2Ereal,type,
j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
thf(j_mono_2Etyop_2Ebinary__ieee_2Erounding,type,
j_mono_2Etyop_2Ebinary__ieee_2Erounding: du > mono_2Etyop_2Ebinary__ieee_2Erounding ).
thf(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ! [V2x_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
thf(reserved_2Eho_2Ei__thm,axiom,
! [A_27a: d,V0x_2E0: u] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(reserved_2Eho_2Ek__thm,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(reserved_2Eho_2Es__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
thf(reserved_2Elogic_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(reserved_2Elogic_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(reserved_2Elogic_2E_7E,axiom,
! [V0: $o] :
( ( mono_2Ec_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(reserved_2Elogic_2E_3D,axiom,
! [A_27a: d,V0_2E0: u,V1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V0_2E0 )
= ( s @ A_27a @ V1_2E0 ) ) ) ).
thf(reserved_2Equant_2E_21,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(reserved_2Equant_2E_3F,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ ( j_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
= ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Ebinary__ieee_2Erounding,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ ( j_mono_2Etyop_2Ebinary__ieee_2Erounding @ ( s @ tyop_2Ebinary__ieee_2Erounding @ V0_2E0 ) ) ) )
= ( s @ tyop_2Ebinary__ieee_2Erounding @ V0_2E0 ) ) ).
thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Ebinary__ieee_2Erounding,axiom,
! [V0: mono_2Etyop_2Ebinary__ieee_2Erounding] :
( ( j_mono_2Etyop_2Ebinary__ieee_2Erounding @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ V0 ) ) )
= V0 ) ).
thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1: $o] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EFINITE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
! [A_27t: d,A_27w: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EFINITE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ewords_2EINT__MAX_2E1_2Emono_2EA_27w,axiom,
! [A_27w: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2EINT__MAX_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27w ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A_27w ) @ tyop_2Enum_2Enum ) @ c_2Ewords_2EINT__MAX_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ A_27w ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
! [A_27t: d,A_27w: d,X0_2E0: u] :
( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebinary__ieee_2Eclosest__such_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X2 ) ) ) )
= ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) ) ) @ c_2Ebinary__ieee_2Eclosest__such_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X2 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27t,axiom,
! [A_27t: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efcp_2Edimindex_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27t ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A_27t ) @ tyop_2Enum_2Enum ) @ c_2Efcp_2Edimindex_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ A_27t ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Elift__ieee_2Eerror_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0_2E0: u,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ c_2Elift__ieee_2Eerror_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) @ X1 ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( c_2Ebinary__ieee_2Efloat__Sign_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) ) @ c_2Ebinary__ieee_2Efloat__Sign_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ebinary__ieee_2Efloat__add_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__add_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) @ c_2Ebinary__ieee_2Efloat__add_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebinary__ieee_2Efloat__div_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__div_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) @ c_2Ebinary__ieee_2Efloat__div_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebinary__ieee_2Efloat__equal_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__equal_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebinary__ieee_2Efloat__equal_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebinary__ieee_2Efloat__greater__equal_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__greater__equal_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebinary__ieee_2Efloat__greater__equal_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebinary__ieee_2Efloat__greater__than_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__greater__than_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebinary__ieee_2Efloat__greater__than_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__finite_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Ebinary__ieee_2Efloat__is__finite_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__finite_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ tyop_2Emin_2Ebool ) @ c_2Ebinary__ieee_2Efloat__is__finite_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__nan_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__nan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Ebinary__ieee_2Efloat__is__nan_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__zero_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__zero_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Ebinary__ieee_2Efloat__is__zero_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__zero_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ tyop_2Emin_2Ebool ) @ c_2Ebinary__ieee_2Efloat__is__zero_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebinary__ieee_2Efloat__less__equal_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__less__equal_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebinary__ieee_2Efloat__less__equal_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebinary__ieee_2Efloat__less__than_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__less__than_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebinary__ieee_2Efloat__less__than_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ebinary__ieee_2Efloat__mul_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) @ c_2Ebinary__ieee_2Efloat__mul_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__add_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__add_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X3_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) ) @ c_2Ebinary__ieee_2Efloat__mul__add_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X3_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__sub_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__sub_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X3_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) ) @ c_2Ebinary__ieee_2Efloat__mul__sub_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X3_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1: $o,X2: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Efloat__round_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X2 ) ) ) )
= ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) ) ) @ c_2Ebinary__ieee_2Efloat__round_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X2 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1: $o,X2: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__round_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X2 ) ) ) )
= ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) @ c_2Ebinary__ieee_2Efloat__round_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X2 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebinary__ieee_2Efloat__sqrt_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sqrt_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) @ c_2Ebinary__ieee_2Efloat__sqrt_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebinary__ieee_2Efloat__sub_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sub_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) ) ) @ c_2Ebinary__ieee_2Efloat__sub_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ebinary__ieee_2Eis__closest_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Erealax_2Ereal,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Eis__closest_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Ebinary__ieee_2Eis__closest_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Elargest_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Elargest_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Elargest_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Elift__ieee_2Enormalizes_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0_2E0: u,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elift__ieee_2Enormalizes_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ c_2Elift__ieee_2Enormalizes_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) @ X1 ) ) ).
thf(arityeq2_2Ec_2Ebinary__ieee_2Ereal__to__float_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Ereal__to__float_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) ) )
= ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) ) @ c_2Ebinary__ieee_2Ereal__to__float_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebinary__ieee_2Eround_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Eround_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) ) )
= ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) ) @ c_2Ebinary__ieee_2Eround_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebinary__ieee_2Eround_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Eround_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) ) )
= ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ebinary__ieee_2Erounding @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) ) @ c_2Ebinary__ieee_2Eround_2E0 ) @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ X0 ) ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Ethreshold_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Ethreshold_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Ethreshold_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t: d,A_27w: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Ethreshold_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ewords_2En2w_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29 @ mono_2Ec_2Ewords_2En2w_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) ) @ c_2Ewords_2En2w_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ ( mono_2Ec_2Ewords_2En2w_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) ) ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Elift__ieee_2Eerror__def,axiom,
! [A_27t: d,A_27w: d,V0x: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0x ) ) ) ) )
= ( mono_2Ec_2Ereal_2Ereal__sub @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Eround_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0x ) ) ) ) ) ) ) @ V0x ) ) ).
thf(thm_2Elift__ieee_2Enormalizes__def,axiom,
! [A_27t: d,A_27w: d,V0x: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elift__ieee_2Enormalizes_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0x ) ) ) ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2EINT__MAX_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27w ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
& ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Einv @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2D @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2EINT__MAX_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27w ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( mono_2Ec_2Ereal_2Eabs @ V0x ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ V0x ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__lt,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__less__than_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__le,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__less__equal_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) )
= ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__gt,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__greater__than_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) )
= ( mono_2Ec_2Ereal_2Ereal__gt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__ge,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__greater__equal_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) )
= ( mono_2Ec_2Ereal_2Ereal__ge @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__eq,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__equal_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) )
<=> ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V1y_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__eq__refl,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__equal_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) )
<=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__nan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Eis__closest__exits,axiom,
! [A_27a: d,A_27b: d,V0x: mono_2Etyop_2Erealax_2Ereal,V1s_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) )
=> ( ( (~)
@ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
=> ? [V2a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Eis__closest_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0x ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V2a_2E0 ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Eclosest__is__everything,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u,V1s_2E0: u,V2x: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) )
=> ( ( (~)
@ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Eis__closest_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0p_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x ) ) ) ) ) ) )
& ( ? [V3b_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Eis__closest_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V3b_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0p_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V3b_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0p_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0p_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Eclosest__in__set,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u,V1s_2E0: u,V2x: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) )
=> ( ( (~)
@ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0p_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Eclosest__is__closest,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u,V1s_2E0: u,V2x: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) )
=> ( ( (~)
@ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Eis__closest_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0p_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__finite,axiom,
! [A_27t: d,A_27w: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) ) ).
thf(thm_2Elift__ieee_2Eis__finite__finite,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0a_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0a_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0a_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0a_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Eis__finite__nonempty,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0a_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0a_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0a_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0a_2E0 ) ) ) ) ) )
=> ( (~)
@ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ).
thf(thm_2Elift__ieee_2Eis__finite__closest,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V2a_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V2a_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V2a_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V2a_2E0 ) ) ) ) ) )
=> ! [V0p_2E0: u,V1x: mono_2Etyop_2Erealax_2Ereal] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0p_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1x ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__to__real__finite,axiom,
! [A_27t: d,A_27w: d,V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0x_2E0 ) ) ) )
=> ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0x_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Elargest_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__to__real__threshold,axiom,
! [A_27t: d,A_27w: d,V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0x_2E0 ) ) ) )
=> ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0x_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Eerror__at__worst__lemma,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1x: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ V1x ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) )
=> ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1x ) ) ) ) ) ) @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ V1x ) ) ) ) ).
thf(thm_2Elift__ieee_2Eerror__is__zero,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1x: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
= V1x ) )
=> ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1x ) ) ) ) )
= ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Elift__ieee_2Erelative__error,axiom,
! [A_27t: d,A_27w: d,V0x: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elift__ieee_2Enormalizes_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0x ) ) ) ) )
=> ? [V1e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ V1e ) @ ( mono_2Ec_2Ereal_2E_2F @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efcp_2Edimindex_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27t ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Eround_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0x ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ V0x @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V1e ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__round__finite,axiom,
! [A_27t: d,A_27w: d,V0b: $o,V1x: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ V1x ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__round_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0b ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1x ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__add,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__add_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__add_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__sub,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sub_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sub_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__mul,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__div,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__zero_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Ereal_2E_2F @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__div_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__div_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2E_2F @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2E_2F @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__sqrt,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( ( j_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( c_2Ebinary__ieee_2Efloat__Sign_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
= ( mono_2Ec_2Ewords_2En2w_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Enum_2E0 ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Etransc_2Esqrt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sqrt_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sqrt_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Etransc_2Esqrt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Etransc_2Esqrt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__mul__add,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__add_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__add_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__mul__sub,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__sub_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__sub_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Elift__ieee_2Eerror_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__add__finite,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__add_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__sub__finite,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sub_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__mul__finite,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__div__finite,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__zero_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Ereal_2E_2F @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__div_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__sqrt__finite,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( ( j_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( c_2Ebinary__ieee_2Efloat__Sign_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
= ( mono_2Ec_2Ewords_2En2w_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Enum_2E0 ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Etransc_2Esqrt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sqrt_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__mul__add__finite,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__add_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__mul__sub__finite,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__sub_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__add__relative,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elift__ieee_2Enormalizes_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__add_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
& ? [V2e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ V2e ) @ ( mono_2Ec_2Ereal_2E_2F @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efcp_2Edimindex_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27t ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__add_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__sub__relative,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elift__ieee_2Enormalizes_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sub_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
& ? [V2e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ V2e ) @ ( mono_2Ec_2Ereal_2E_2F @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efcp_2Edimindex_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27t ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sub_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__mul__relative,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elift__ieee_2Enormalizes_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
& ? [V2e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ V2e ) @ ( mono_2Ec_2Ereal_2E_2F @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efcp_2Edimindex_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27t ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__div__relative,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__zero_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elift__ieee_2Enormalizes_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2E_2F @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__div_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
& ? [V2e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ V2e ) @ ( mono_2Ec_2Ereal_2E_2F @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efcp_2Edimindex_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27t ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__div_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Ereal_2E_2F @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V2e ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__sqrt__relative,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( ( j_mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ tyop_2Eone_2Eone ) @ ( c_2Ebinary__ieee_2Efloat__Sign_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
= ( mono_2Ec_2Ewords_2En2w_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Enum_2E0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elift__ieee_2Enormalizes_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Etransc_2Esqrt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sqrt_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) ) ) )
& ? [V1e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ V1e ) @ ( mono_2Ec_2Ereal_2E_2F @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efcp_2Edimindex_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27t ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__sqrt_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Etransc_2Esqrt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V1e ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__mul__add__relative,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elift__ieee_2Enormalizes_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__add_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) )
& ? [V3e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ V3e ) @ ( mono_2Ec_2Ereal_2E_2F @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efcp_2Edimindex_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27t ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__add_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V3e ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__mul__sub__relative,axiom,
! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elift__ieee_2Enormalizes_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__sub_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) )
& ? [V3e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ V3e ) @ ( mono_2Ec_2Ereal_2E_2F @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efcp_2Edimindex_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27t ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Ebinary__ieee_2Eflags @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ ( c_2Ebinary__ieee_2Efloat__mul__sub_2E4 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V0a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V1b_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ V2c_2E0 ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V3e ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Efinite__float__within__threshold,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) )
=> ( ( (~) @ ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
& ( (~) @ ( mono_2Ec_2Ereal_2Ereal__ge @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Elift__ieee_2Eround__finite__normal__float__id,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) )
& ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__zero_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
=> ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Eround_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ).
thf(thm_2Elift__ieee_2Ereal__to__float__finite__normal__id,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__finite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) )
& ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__zero_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
=> ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Ereal__to__float_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ).
thf(thm_2Elift__ieee_2Efloat__to__real__real__to__float__zero__id,axiom,
! [A_27a: d,A_27b: d] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Ereal__to__float_2E2 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Elift__ieee_2Enon__representable__float__is__zero,axiom,
! [A_27a: d,A_27b: d,V0ff: mono_2Etyop_2Erealax_2Ereal,V1P: $o] :
( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Eabs @ V0ff ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Efloat__round_2E3 @ ( s @ tyop_2Ebinary__ieee_2Erounding @ ( i_mono_2Etyop_2Ebinary__ieee_2Erounding @ mono_2Ec_2Ebinary__ieee_2EroundTiesToEven ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1P ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0ff ) ) ) ) ) ) )
= ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
%------------------------------------------------------------------------------