%------------------------------------------------------------------------------
% 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    :  457 ( 123 unt; 274 typ;   0 def)
%            Number of atoms       :  343 ( 163 equ)
%            Maximal formula atoms :    7 (   0 avg)
%            Number of connectives :  176 (  16   ~;   3   |;  89   &)
%                                         (  16 <=>;  52  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :   16 (   3 avg)
%            Number of types       :   22 (  21 usr)
%            Number of type conns  :  226 ( 144   >;  82   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  252 ( 252 usr; 109 con; 0-4 aty)
%            Number of variables   :  499 ( 488   !;  11   ?; 499   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(u,type,
    u: $tType ).

tff(d,type,
    d: $tType ).

tff(du,type,
    du: $tType ).

tff(mono_2Etyop_2Emin_2Ebool,type,
    mono_2Etyop_2Emin_2Ebool: $tType ).

tff(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,type,
    mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).

tff(mono_2Etyop_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

tff(mono_2Etyop_2Erealax_2Ereal,type,
    mono_2Etyop_2Erealax_2Ereal: $tType ).

tff(mono_2Etyop_2Ebinary__ieee_2Erounding,type,
    mono_2Etyop_2Ebinary__ieee_2Erounding: $tType ).

tff(tyop_2Ebinary__ieee_2Eflags,type,
    tyop_2Ebinary__ieee_2Eflags: d ).

tff(tyop_2Ebinary__ieee_2Efloat,type,
    tyop_2Ebinary__ieee_2Efloat: ( d * d ) > d ).

tff(tyop_2Ebinary__ieee_2Erounding,type,
    tyop_2Ebinary__ieee_2Erounding: d ).

tff(tyop_2Ebool_2Eitself,type,
    tyop_2Ebool_2Eitself: d > d ).

tff(tyop_2Efcp_2Ecart,type,
    tyop_2Efcp_2Ecart: ( d * d ) > d ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( d * d ) > d ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

tff(tyop_2Eone_2Eone,type,
    tyop_2Eone_2Eone: d ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( d * d ) > d ).

tff(tyop_2Erealax_2Ereal,type,
    tyop_2Erealax_2Ereal: d ).

tff(s,type,
    s: ( d * u ) > du ).

tff(app_2E2,type,
    app_2E2: ( du * du ) > u ).

tff(p,type,
    p: mono_2Etyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: u ).

tff(combin_k_2E0,type,
    combin_k_2E0: u ).

tff(combin_s_2E0,type,
    combin_s_2E0: u ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: du > u ).

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: u ).

tff(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: ( du * du ) > u ).

tff(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: u ).

tff(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: ( du * du ) > u ).

tff(c_2Ereal_2E_2F_2E0,type,
    c_2Ereal_2E_2F_2E0: u ).

tff(c_2Ereal_2E_2F_2E2,type,
    c_2Ereal_2E_2F_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: u ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: du > u ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: u ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: du > u ).

tff(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: u ).

tff(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: du > u ).

tff(c_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: u ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

tff(c_2Epred__set_2EFINITE_2E0,type,
    c_2Epred__set_2EFINITE_2E0: u ).

tff(c_2Epred__set_2EFINITE_2E1,type,
    c_2Epred__set_2EFINITE_2E1: du > u ).

tff(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: u ).

tff(c_2Epred__set_2EGSPEC_2E1,type,
    c_2Epred__set_2EGSPEC_2E1: du > u ).

tff(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

tff(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: ( du * du ) > u ).

tff(c_2Ewords_2EINT__MAX_2E0,type,
    c_2Ewords_2EINT__MAX_2E0: u ).

tff(c_2Ewords_2EINT__MAX_2E1,type,
    c_2Ewords_2EINT__MAX_2E1: du > u ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: du > u ).

tff(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: u ).

tff(c_2Epair_2ESND_2E1,type,
    c_2Epair_2ESND_2E1: du > u ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

tff(c_2Epred__set_2EUNIV_2E0,type,
    c_2Epred__set_2EUNIV_2E0: u ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).

tff(c_2Ereal_2Eabs_2E0,type,
    c_2Ereal_2Eabs_2E0: u ).

tff(c_2Ereal_2Eabs_2E1,type,
    c_2Ereal_2Eabs_2E1: du > u ).

tff(c_2Ebinary__ieee_2Eclosest__such_2E0,type,
    c_2Ebinary__ieee_2Eclosest__such_2E0: u ).

tff(c_2Ebinary__ieee_2Eclosest__such_2E3,type,
    c_2Ebinary__ieee_2Eclosest__such_2E3: ( du * du * du ) > u ).

tff(c_2Efcp_2Edimindex_2E0,type,
    c_2Efcp_2Edimindex_2E0: u ).

tff(c_2Efcp_2Edimindex_2E1,type,
    c_2Efcp_2Edimindex_2E1: du > u ).

tff(c_2Elift__ieee_2Eerror_2E0,type,
    c_2Elift__ieee_2Eerror_2E0: u ).

tff(c_2Elift__ieee_2Eerror_2E2,type,
    c_2Elift__ieee_2Eerror_2E2: ( du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__Sign_2E0,type,
    c_2Ebinary__ieee_2Efloat__Sign_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__Sign_2E1,type,
    c_2Ebinary__ieee_2Efloat__Sign_2E1: du > u ).

tff(c_2Ebinary__ieee_2Efloat__add_2E0,type,
    c_2Ebinary__ieee_2Efloat__add_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__add_2E3,type,
    c_2Ebinary__ieee_2Efloat__add_2E3: ( du * du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__div_2E0,type,
    c_2Ebinary__ieee_2Efloat__div_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__div_2E3,type,
    c_2Ebinary__ieee_2Efloat__div_2E3: ( du * du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__equal_2E0,type,
    c_2Ebinary__ieee_2Efloat__equal_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__equal_2E2,type,
    c_2Ebinary__ieee_2Efloat__equal_2E2: ( du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__greater__equal_2E0,type,
    c_2Ebinary__ieee_2Efloat__greater__equal_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__greater__equal_2E2,type,
    c_2Ebinary__ieee_2Efloat__greater__equal_2E2: ( du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__greater__than_2E0,type,
    c_2Ebinary__ieee_2Efloat__greater__than_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__greater__than_2E2,type,
    c_2Ebinary__ieee_2Efloat__greater__than_2E2: ( du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__is__finite_2E0,type,
    c_2Ebinary__ieee_2Efloat__is__finite_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__is__finite_2E1,type,
    c_2Ebinary__ieee_2Efloat__is__finite_2E1: du > u ).

tff(c_2Ebinary__ieee_2Efloat__is__nan_2E0,type,
    c_2Ebinary__ieee_2Efloat__is__nan_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__is__nan_2E1,type,
    c_2Ebinary__ieee_2Efloat__is__nan_2E1: du > u ).

tff(c_2Ebinary__ieee_2Efloat__is__zero_2E0,type,
    c_2Ebinary__ieee_2Efloat__is__zero_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__is__zero_2E1,type,
    c_2Ebinary__ieee_2Efloat__is__zero_2E1: du > u ).

tff(c_2Ebinary__ieee_2Efloat__less__equal_2E0,type,
    c_2Ebinary__ieee_2Efloat__less__equal_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__less__equal_2E2,type,
    c_2Ebinary__ieee_2Efloat__less__equal_2E2: ( du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__less__than_2E0,type,
    c_2Ebinary__ieee_2Efloat__less__than_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__less__than_2E2,type,
    c_2Ebinary__ieee_2Efloat__less__than_2E2: ( du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__mul_2E0,type,
    c_2Ebinary__ieee_2Efloat__mul_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__mul_2E3,type,
    c_2Ebinary__ieee_2Efloat__mul_2E3: ( du * du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__mul__add_2E0,type,
    c_2Ebinary__ieee_2Efloat__mul__add_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__mul__add_2E4,type,
    c_2Ebinary__ieee_2Efloat__mul__add_2E4: ( du * du * du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__mul__sub_2E0,type,
    c_2Ebinary__ieee_2Efloat__mul__sub_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__mul__sub_2E4,type,
    c_2Ebinary__ieee_2Efloat__mul__sub_2E4: ( du * du * du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__round_2E0,type,
    c_2Ebinary__ieee_2Efloat__round_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__round_2E3,type,
    c_2Ebinary__ieee_2Efloat__round_2E3: ( du * du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__sqrt_2E0,type,
    c_2Ebinary__ieee_2Efloat__sqrt_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__sqrt_2E2,type,
    c_2Ebinary__ieee_2Efloat__sqrt_2E2: ( du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__sub_2E0,type,
    c_2Ebinary__ieee_2Efloat__sub_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__sub_2E3,type,
    c_2Ebinary__ieee_2Efloat__sub_2E3: ( du * du * du ) > u ).

tff(c_2Ebinary__ieee_2Efloat__to__real_2E0,type,
    c_2Ebinary__ieee_2Efloat__to__real_2E0: u ).

tff(c_2Ebinary__ieee_2Efloat__to__real_2E1,type,
    c_2Ebinary__ieee_2Efloat__to__real_2E1: du > u ).

tff(c_2Erealax_2Einv_2E0,type,
    c_2Erealax_2Einv_2E0: u ).

tff(c_2Erealax_2Einv_2E1,type,
    c_2Erealax_2Einv_2E1: du > u ).

tff(c_2Ebinary__ieee_2Eis__closest_2E0,type,
    c_2Ebinary__ieee_2Eis__closest_2E0: u ).

tff(c_2Ebinary__ieee_2Eis__closest_2E3,type,
    c_2Ebinary__ieee_2Eis__closest_2E3: ( du * du * du ) > u ).

tff(c_2Ebinary__ieee_2Elargest_2E0,type,
    c_2Ebinary__ieee_2Elargest_2E0: u ).

tff(c_2Ebinary__ieee_2Elargest_2E1,type,
    c_2Ebinary__ieee_2Elargest_2E1: du > u ).

tff(c_2Ewords_2En2w_2E0,type,
    c_2Ewords_2En2w_2E0: u ).

tff(c_2Ewords_2En2w_2E1,type,
    c_2Ewords_2En2w_2E1: du > u ).

tff(c_2Elift__ieee_2Enormalizes_2E0,type,
    c_2Elift__ieee_2Enormalizes_2E0: u ).

tff(c_2Elift__ieee_2Enormalizes_2E2,type,
    c_2Elift__ieee_2Enormalizes_2E2: ( du * du ) > u ).

tff(c_2Ereal_2Epow_2E0,type,
    c_2Ereal_2Epow_2E0: u ).

tff(c_2Ereal_2Epow_2E2,type,
    c_2Ereal_2Epow_2E2: ( du * du ) > u ).

tff(c_2Erealax_2Ereal__add_2E0,type,
    c_2Erealax_2Ereal__add_2E0: u ).

tff(c_2Erealax_2Ereal__add_2E2,type,
    c_2Erealax_2Ereal__add_2E2: ( du * du ) > u ).

tff(c_2Ereal_2Ereal__ge_2E0,type,
    c_2Ereal_2Ereal__ge_2E0: u ).

tff(c_2Ereal_2Ereal__ge_2E2,type,
    c_2Ereal_2Ereal__ge_2E2: ( du * du ) > u ).

tff(c_2Ereal_2Ereal__gt_2E0,type,
    c_2Ereal_2Ereal__gt_2E0: u ).

tff(c_2Ereal_2Ereal__gt_2E2,type,
    c_2Ereal_2Ereal__gt_2E2: ( du * du ) > u ).

tff(c_2Erealax_2Ereal__lt_2E0,type,
    c_2Erealax_2Ereal__lt_2E0: u ).

tff(c_2Erealax_2Ereal__lt_2E2,type,
    c_2Erealax_2Ereal__lt_2E2: ( du * du ) > u ).

tff(c_2Ereal_2Ereal__lte_2E0,type,
    c_2Ereal_2Ereal__lte_2E0: u ).

tff(c_2Ereal_2Ereal__lte_2E2,type,
    c_2Ereal_2Ereal__lte_2E2: ( du * du ) > u ).

tff(c_2Erealax_2Ereal__mul_2E0,type,
    c_2Erealax_2Ereal__mul_2E0: u ).

tff(c_2Erealax_2Ereal__mul_2E2,type,
    c_2Erealax_2Ereal__mul_2E2: ( du * du ) > u ).

tff(c_2Erealax_2Ereal__neg_2E0,type,
    c_2Erealax_2Ereal__neg_2E0: u ).

tff(c_2Erealax_2Ereal__neg_2E1,type,
    c_2Erealax_2Ereal__neg_2E1: du > u ).

tff(c_2Ereal_2Ereal__of__num_2E0,type,
    c_2Ereal_2Ereal__of__num_2E0: u ).

tff(c_2Ereal_2Ereal__of__num_2E1,type,
    c_2Ereal_2Ereal__of__num_2E1: du > u ).

tff(c_2Ereal_2Ereal__sub_2E0,type,
    c_2Ereal_2Ereal__sub_2E0: u ).

tff(c_2Ereal_2Ereal__sub_2E2,type,
    c_2Ereal_2Ereal__sub_2E2: ( du * du ) > u ).

tff(c_2Ebinary__ieee_2Ereal__to__float_2E0,type,
    c_2Ebinary__ieee_2Ereal__to__float_2E0: u ).

tff(c_2Ebinary__ieee_2Ereal__to__float_2E2,type,
    c_2Ebinary__ieee_2Ereal__to__float_2E2: ( du * du ) > u ).

tff(c_2Ebinary__ieee_2Eround_2E0,type,
    c_2Ebinary__ieee_2Eround_2E0: u ).

tff(c_2Ebinary__ieee_2Eround_2E2,type,
    c_2Ebinary__ieee_2Eround_2E2: ( du * du ) > u ).

tff(c_2Ebinary__ieee_2EroundTiesToEven_2E0,type,
    c_2Ebinary__ieee_2EroundTiesToEven_2E0: u ).

tff(c_2Etransc_2Esqrt_2E0,type,
    c_2Etransc_2Esqrt_2E0: u ).

tff(c_2Etransc_2Esqrt_2E1,type,
    c_2Etransc_2Esqrt_2E1: du > u ).

tff(c_2Ebool_2Ethe__value_2E0,type,
    c_2Ebool_2Ethe__value_2E0: u ).

tff(c_2Ebinary__ieee_2Ethreshold_2E0,type,
    c_2Ebinary__ieee_2Ethreshold_2E0: u ).

tff(c_2Ebinary__ieee_2Ethreshold_2E1,type,
    c_2Ebinary__ieee_2Ethreshold_2E1: du > u ).

tff(c_2Ebinary__ieee_2Eulp_2E0,type,
    c_2Ebinary__ieee_2Eulp_2E0: u ).

tff(c_2Ebinary__ieee_2Eulp_2E1,type,
    c_2Ebinary__ieee_2Eulp_2E1: du > u ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: du > u ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29: ( 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 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Earithmetic_2E_2B_2E0,type,
    mono_2Ec_2Earithmetic_2E_2B_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2B_2E2,type,
    mono_2Ec_2Earithmetic_2E_2B_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2E_2D_2E0,type,
    mono_2Ec_2Earithmetic_2E_2D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2D_2E2,type,
    mono_2Ec_2Earithmetic_2E_2D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ereal_2E_2F_2E0,type,
    mono_2Ec_2Ereal_2E_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).

tff(mono_2Ec_2Ereal_2E_2F_2E2,type,
    mono_2Ec_2Ereal_2E_2F_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E0,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E2,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Enum_2E0_2E0,type,
    mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E0,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E2,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E2,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2EBIT1_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EBIT1_2E1,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2EBIT2_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EBIT2_2E1,type,
    mono_2Ec_2Earithmetic_2EBIT2_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2EF_2E0,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2ENUMERAL_2E0,type,
    mono_2Ec_2Earithmetic_2ENUMERAL_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2ENUMERAL_2E1,type,
    mono_2Ec_2Earithmetic_2ENUMERAL_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2ET_2E0,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2EZERO_2E0,type,
    mono_2Ec_2Earithmetic_2EZERO_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E0,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E2,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ereal_2Eabs_2E0,type,
    mono_2Ec_2Ereal_2Eabs_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

tff(mono_2Ec_2Ereal_2Eabs_2E1,type,
    mono_2Ec_2Ereal_2Eabs_2E1: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Erealax_2Einv_2E0,type,
    mono_2Ec_2Erealax_2Einv_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

tff(mono_2Ec_2Erealax_2Einv_2E1,type,
    mono_2Ec_2Erealax_2Einv_2E1: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Ewords_2En2w_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Ewords_2En2w_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29 ).

tff(mono_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Ereal_2Epow_2E0,type,
    mono_2Ec_2Ereal_2Epow_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 ).

tff(mono_2Ec_2Ereal_2Epow_2E2,type,
    mono_2Ec_2Ereal_2Epow_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Erealax_2Ereal__add_2E0,type,
    mono_2Ec_2Erealax_2Ereal__add_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).

tff(mono_2Ec_2Erealax_2Ereal__add_2E2,type,
    mono_2Ec_2Erealax_2Ereal__add_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Ereal_2Ereal__ge_2E0,type,
    mono_2Ec_2Ereal_2Ereal__ge_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ereal_2Ereal__ge_2E2,type,
    mono_2Ec_2Ereal_2Ereal__ge_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ereal_2Ereal__gt_2E0,type,
    mono_2Ec_2Ereal_2Ereal__gt_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ereal_2Ereal__gt_2E2,type,
    mono_2Ec_2Ereal_2Ereal__gt_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Erealax_2Ereal__lt_2E0,type,
    mono_2Ec_2Erealax_2Ereal__lt_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Erealax_2Ereal__lt_2E2,type,
    mono_2Ec_2Erealax_2Ereal__lt_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ereal_2Ereal__lte_2E0,type,
    mono_2Ec_2Ereal_2Ereal__lte_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ereal_2Ereal__lte_2E2,type,
    mono_2Ec_2Ereal_2Ereal__lte_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Erealax_2Ereal__mul_2E0,type,
    mono_2Ec_2Erealax_2Ereal__mul_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).

tff(mono_2Ec_2Erealax_2Ereal__mul_2E2,type,
    mono_2Ec_2Erealax_2Ereal__mul_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Erealax_2Ereal__neg_2E0,type,
    mono_2Ec_2Erealax_2Ereal__neg_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

tff(mono_2Ec_2Erealax_2Ereal__neg_2E1,type,
    mono_2Ec_2Erealax_2Ereal__neg_2E1: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Ereal_2Ereal__of__num_2E0,type,
    mono_2Ec_2Ereal_2Ereal__of__num_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 ).

tff(mono_2Ec_2Ereal_2Ereal__of__num_2E1,type,
    mono_2Ec_2Ereal_2Ereal__of__num_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Ereal_2Ereal__sub_2E0,type,
    mono_2Ec_2Ereal_2Ereal__sub_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).

tff(mono_2Ec_2Ereal_2Ereal__sub_2E2,type,
    mono_2Ec_2Ereal_2Ereal__sub_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Ebinary__ieee_2EroundTiesToEven_2E0,type,
    mono_2Ec_2Ebinary__ieee_2EroundTiesToEven_2E0: mono_2Etyop_2Ebinary__ieee_2Erounding ).

tff(mono_2Ec_2Etransc_2Esqrt_2E0,type,
    mono_2Ec_2Etransc_2Esqrt_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

tff(mono_2Ec_2Etransc_2Esqrt_2E1,type,
    mono_2Ec_2Etransc_2Esqrt_2E1: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

tff(mono_2Ec_2Ebool_2E_7E_2E0,type,
    mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2E_7E_2E1,type,
    mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

tff(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).

tff(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 ).

tff(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: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).

tff(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: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).

tff(i_mono_2Etyop_2Enum_2Enum,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

tff(i_mono_2Etyop_2Erealax_2Ereal,type,
    i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).

tff(i_mono_2Etyop_2Ebinary__ieee_2Erounding,type,
    i_mono_2Etyop_2Ebinary__ieee_2Erounding: mono_2Etyop_2Ebinary__ieee_2Erounding > u ).

tff(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).

tff(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 ).

tff(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 > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(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 > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 ).

tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).

tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

tff(j_mono_2Etyop_2Enum_2Enum,type,
    j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).

tff(j_mono_2Etyop_2Erealax_2Ereal,type,
    j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).

tff(j_mono_2Etyop_2Ebinary__ieee_2Erounding,type,
    j_mono_2Etyop_2Ebinary__ieee_2Erounding: du > mono_2Etyop_2Ebinary__ieee_2Erounding ).

tff(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) ) ) ).

tff(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(reserved_2Eho_2Etruth,axiom,
    p(mono_2Ec_2Ebool_2ET_2E0) ).

tff(reserved_2Eho_2Enotfalse,axiom,
    ~ p(mono_2Ec_2Ebool_2EF_2E0) ).

tff(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = mono_2Ec_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = mono_2Ec_2Ebool_2EF_2E0 ) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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))))) ) ).

tff(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
      ( p(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) ) ) ).

tff(reserved_2Equant_2E_21,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(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] : p(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))))) ) ).

tff(reserved_2Equant_2E_3F,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(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] : p(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))))) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: 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_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0_2E0: mono_2Etyop_2Erealax_2Ereal] : ( j_mono_2Etyop_2Erealax_2Ereal(s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Ebinary__ieee_2Erounding,axiom,
    ! [V0_2E0: mono_2Etyop_2Ebinary__ieee_2Erounding] : ( j_mono_2Etyop_2Ebinary__ieee_2Erounding(s(tyop_2Ebinary__ieee_2Erounding,i_mono_2Etyop_2Ebinary__ieee_2Erounding(V0_2E0))) = V0_2E0 ) ).

tff(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)))) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).

tff(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_2E0: mono_2Etyop_2Emin_2Ebool] : ( 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_2E0)))) = 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_2E0)))) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ereal_2E_2F_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal_2E_2F_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ereal_2E_2F_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(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) )
    <=> p(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))))) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(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)))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT1_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT2_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(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))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(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))) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ereal_2Eabs_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal_2Eabs_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal_2Eabs_2E0,X0_2E0) ) ).

tff(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_2E0: 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_2E0)))) = 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_2E0)))) ) ).

tff(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)))) ) ).

tff(arityeq2_2Ec_2Elift__ieee_2Eerror_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: u,X1_2E0: 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_2E0))))) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_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),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_2E0) ) ).

tff(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)))) ) ).

tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__add_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: 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_2E0)),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_2E0)))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__div_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: 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_2E0)),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_2E0)))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__mul_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: 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_2E0)),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_2E0)))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ) ).

tff(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__add_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: 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_2E0)),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_2E0)))),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))) ) ).

tff(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__sub_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: 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_2E0)),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_2E0)))),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))) ) ).

tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: mono_2Etyop_2Emin_2Ebool,X2_2E0: 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_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(X2_2E0)))) = 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_2E0)))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: mono_2Etyop_2Emin_2Ebool,X2_2E0: 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_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(X2_2E0)))) = 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_2E0)))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(X2_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebinary__ieee_2Efloat__sqrt_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: 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_2E0)),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_2E0)))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Ebinary__ieee_2Efloat__sub_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: 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_2E0)),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_2E0)))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(arityeq1_2Ec_2Erealax_2Einv_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Erealax_2Einv_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Erealax_2Einv_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebinary__ieee_2Eis__closest_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: 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_2E0)),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_2E0)))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0)))) ) ).

tff(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)))) ) ).

tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29(mono_2Ec_2Ewords_2En2w_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0) ) ).

tff(arityeq2_2Ec_2Elift__ieee_2Enormalizes_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: u,X1_2E0: 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_2E0))))) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool(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_2E0) ) ).

tff(arityeq2_2Ec_2Ereal_2Epow_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ereal_2Epow_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ereal_2Epow_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Erealax_2Ereal__add_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Erealax_2Ereal__add_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ereal_2Ereal__ge_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal_2Ereal__ge_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal_2Ereal__ge_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ereal_2Ereal__gt_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal_2Ereal__gt_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal_2Ereal__gt_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Erealax_2Ereal__lt_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Erealax_2Ereal__lt_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal_2Ereal__lte_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal_2Ereal__lte_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Erealax_2Ereal__mul_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Erealax_2Ereal__mul_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erealax_2Ereal__neg_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Erealax_2Ereal__neg_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Erealax_2Ereal__neg_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ereal_2Ereal__of__num_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal_2Ereal__of__num_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Ereal_2Ereal__sub_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal_2Ereal__sub_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(mono_2Ec_2Ereal_2Ereal__sub_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebinary__ieee_2Ereal__to__float_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(X1_2E0)))) = 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_2E0)))),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebinary__ieee_2Eround_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(X1_2E0)))) = 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_2E0)))),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebinary__ieee_2Eround_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t: d,A_27w: d,X0_2E0: mono_2Etyop_2Ebinary__ieee_2Erounding,X1_2E0: 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(X1_2E0)))) = 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_2E0)))),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Etransc_2Esqrt_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Etransc_2Esqrt_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Etransc_2Esqrt_2E0,X0_2E0) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(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)))) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29,V1_2E0: 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_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: 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(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,V1_2E0: 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(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Erealax_2Ereal] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,V1_2E0: 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(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: 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(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,V1_2E0: 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(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1_2E0: mono_2Etyop_2Erealax_2Ereal] : ( s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V1_2E0)))) ) ).

tff(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_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ewords_2En2w_2E0) ).

tff(monoeq_2Emono_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: 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_2E1_2Emono_2Etyop_2Eone_2Eone(V0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)))) ) ).

tff(thm_2Elift__ieee_2Eerror__def,axiom,
    ! [A_27t: d,A_27w: d,V0x_2E0: 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_2E0))))) = mono_2Ec_2Ereal_2Ereal__sub_2E2(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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V0x_2E0))))))),V0x_2E0) ) ).

tff(thm_2Elift__ieee_2Enormalizes__def,axiom,
    ! [A_27t: d,A_27w: d,V0x_2E0: mono_2Etyop_2Erealax_2Ereal] :
      ( p(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_2E0))))))
    <=> ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),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))))))
        & p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Erealax_2Einv_2E1(mono_2Ec_2Ereal_2Epow_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2E_2D_2E2(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_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),mono_2Ec_2Ereal_2Eabs_2E1(V0x_2E0)))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(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)))))) ) ) ).

tff(thm_2Elift__ieee_2Efloat__lt,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( p(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)))))
        & p(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_2E2(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))))) ) ) ).

tff(thm_2Elift__ieee_2Efloat__le,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( p(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)))))
        & p(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_2E2(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))))) ) ) ).

tff(thm_2Elift__ieee_2Efloat__gt,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( p(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)))))
        & p(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_2E2(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))))) ) ) ).

tff(thm_2Elift__ieee_2Efloat__ge,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( p(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)))))
        & p(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_2E2(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))))) ) ) ).

tff(thm_2Elift__ieee_2Efloat__eq,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( p(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)))))
        & p(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))))) )
     => ( p(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)))) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__eq__refl,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u] :
      ( p(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)))))
    <=> ~ p(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))))) ) ).

tff(thm_2Elift__ieee_2Eis__closest__exits,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: mono_2Etyop_2Erealax_2Ereal,V1s_2E0: u] :
      ( p(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] : p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2a_2E0))))) ) ) ).

tff(thm_2Elift__ieee_2Eclosest__is__everything,axiom,
    ! [A_27a: d,A_27b: d,V0p_2E0: u,V1s_2E0: u,V2x_2E0: mono_2Etyop_2Erealax_2Ereal] :
      ( p(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) )
       => ( p(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_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_2E0))))))))
          & ( ? [V3b_2E0: u] :
                ( p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V3b_2E0)))))
                & p(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))))) )
           => p(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_2E0)))))))) ) ) ) ) ).

tff(thm_2Elift__ieee_2Eclosest__in__set,axiom,
    ! [A_27a: d,A_27b: d,V0p_2E0: u,V1s_2E0: u,V2x_2E0: mono_2Etyop_2Erealax_2Ereal] :
      ( p(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) )
       => p(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_2E0)))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0))))) ) ) ).

tff(thm_2Elift__ieee_2Eclosest__is__closest,axiom,
    ! [A_27a: d,A_27b: d,V0p_2E0: u,V1s_2E0: u,V2x_2E0: mono_2Etyop_2Erealax_2Ereal] :
      ( p(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) )
       => p(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_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_2E0)))))))) ) ) ).

tff(thm_2Elift__ieee_2Efloat__finite,axiom,
    ! [A_27t: d,A_27w: d] : p(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))))) ).

tff(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))))) )
     => p(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))))))) ) ).

tff(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) ) ) ).

tff(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_2E0: mono_2Etyop_2Erealax_2Ereal] : p(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_2E0)))))))) ) ).

tff(thm_2Elift__ieee_2Efloat__to__real__finite,axiom,
    ! [A_27t: d,A_27w: d,V0x_2E0: u] :
      ( p(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)))))
     => p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Eabs_2E1(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)))))) ) ).

tff(thm_2Elift__ieee_2Efloat__to__real__threshold,axiom,
    ! [A_27t: d,A_27w: d,V0x_2E0: u] :
      ( p(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)))))
     => p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(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)))))) ) ).

tff(thm_2Elift__ieee_2Eerror__at__worst__lemma,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1x_2E0: mono_2Etyop_2Erealax_2Ereal] :
      ( ( p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(V1x_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))))))
        & p(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))))) )
     => p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Eabs_2E1(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_2E0)))))),mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Ereal_2Ereal__sub_2E2(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_2E0)))) ) ).

tff(thm_2Elift__ieee_2Eerror__is__zero,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1x_2E0: mono_2Etyop_2Erealax_2Ereal] :
      ( ( p(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_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(V1x_2E0))))) = mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ) ) ).

tff(thm_2Elift__ieee_2Erelative__error,axiom,
    ! [A_27t: d,A_27w: d,V0x_2E0: mono_2Etyop_2Erealax_2Ereal] :
      ( p(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_2E0))))))
     => ? [V1e_2E0: mono_2Etyop_2Erealax_2Ereal] :
          ( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Eabs_2E1(V1e_2E0),mono_2Ec_2Ereal_2E_2F_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Ereal_2Epow_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2E_2B_2E2(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_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_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_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,i_mono_2Etyop_2Ebinary__ieee_2Erounding(mono_2Ec_2Ebinary__ieee_2EroundTiesToEven_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V0x_2E0))))))) = mono_2Ec_2Erealax_2Ereal__mul_2E2(V0x_2E0,mono_2Ec_2Erealax_2Ereal__add_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),V1e_2E0)) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__round__finite,axiom,
    ! [A_27t: d,A_27w: d,V0b_2E0: mono_2Etyop_2Emin_2Ebool,V1x_2E0: mono_2Etyop_2Erealax_2Ereal] :
      ( p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(V1x_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))))))
     => p(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_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0b_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V1x_2E0)))))))) ) ).

tff(thm_2Elift__ieee_2Efloat__add,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Erealax_2Ereal__add_2E2(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)))))) )
     => ( p(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_2E0)),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_2E0)),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_2E2(mono_2Ec_2Erealax_2Ereal__add_2E2(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_2E2(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))))))))))) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__sub,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Ereal_2Ereal__sub_2E2(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)))))) )
     => ( p(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_2E0)),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_2E0)),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_2E2(mono_2Ec_2Ereal_2Ereal__sub_2E2(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_2E2(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))))))))))) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__mul,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Erealax_2Ereal__mul_2E2(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)))))) )
     => ( p(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_2E0)),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_2E0)),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_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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_2E2(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))))))))))) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__div,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & ~ p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Ereal_2E_2F_2E2(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)))))) )
     => ( p(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_2E0)),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_2E0)),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_2E2(mono_2Ec_2Ereal_2E_2F_2E2(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_2E2(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))))))))))) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__sqrt,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u] :
      ( ( p(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_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Enum_2E0_2E0) )
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Etransc_2Esqrt_2E1(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)))))) )
     => ( p(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_2E0)),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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0)))))))) = mono_2Ec_2Erealax_2Ereal__add_2E2(mono_2Ec_2Etransc_2Esqrt_2E1(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_2E1(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))))))))))) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__mul__add,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Erealax_2Ereal__add_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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)))))) )
     => ( p(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_2E0)),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_2E0)),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_2E2(mono_2Ec_2Erealax_2Ereal__add_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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))))))))))) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__mul__sub,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Ereal_2Ereal__sub_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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)))))) )
     => ( p(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_2E0)),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_2E0)),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_2E2(mono_2Ec_2Ereal_2Ereal__sub_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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))))))))))) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__add__finite,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Erealax_2Ereal__add_2E2(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)))))) )
     => p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))))) ) ).

tff(thm_2Elift__ieee_2Efloat__sub__finite,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Ereal_2Ereal__sub_2E2(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)))))) )
     => p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))))) ) ).

tff(thm_2Elift__ieee_2Efloat__mul__finite,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Erealax_2Ereal__mul_2E2(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)))))) )
     => p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))))) ) ).

tff(thm_2Elift__ieee_2Efloat__div__finite,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & ~ p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Ereal_2E_2F_2E2(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)))))) )
     => p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))))) ) ).

tff(thm_2Elift__ieee_2Efloat__sqrt__finite,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u] :
      ( ( p(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_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Enum_2E0_2E0) )
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Etransc_2Esqrt_2E1(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)))))) )
     => p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))))))) ) ).

tff(thm_2Elift__ieee_2Efloat__mul__add__finite,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Erealax_2Ereal__add_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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)))))) )
     => p(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_2E0)),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))))))))) ) ).

tff(thm_2Elift__ieee_2Efloat__mul__sub__finite,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(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)))))
        & p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Eabs_2E1(mono_2Ec_2Ereal_2Ereal__sub_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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)))))) )
     => p(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_2E0)),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))))))))) ) ).

tff(thm_2Elift__ieee_2Efloat__add__relative,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(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_2E2(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))))))))))) )
     => ( p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0)))))))))
        & ? [V2e_2E0: mono_2Etyop_2Erealax_2Ereal] :
            ( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Eabs_2E1(V2e_2E0),mono_2Ec_2Ereal_2E_2F_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Ereal_2Epow_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2E_2B_2E2(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_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_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_2E0)),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_2E2(mono_2Ec_2Erealax_2Ereal__add_2E2(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_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__sub__relative,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(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_2E2(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))))))))))) )
     => ( p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0)))))))))
        & ? [V2e_2E0: mono_2Etyop_2Erealax_2Ereal] :
            ( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Eabs_2E1(V2e_2E0),mono_2Ec_2Ereal_2E_2F_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Ereal_2Epow_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2E_2B_2E2(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_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_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_2E0)),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_2E2(mono_2Ec_2Ereal_2Ereal__sub_2E2(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_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__mul__relative,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(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_2E2(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))))))))))) )
     => ( p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0)))))))))
        & ? [V2e_2E0: mono_2Etyop_2Erealax_2Ereal] :
            ( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Eabs_2E1(V2e_2E0),mono_2Ec_2Ereal_2E_2F_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Ereal_2Epow_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2E_2B_2E2(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_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_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_2E0)),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_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__div__relative,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & ~ p(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)))))
        & p(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_2E2(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))))))))))) )
     => ( p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0)))))))))
        & ? [V2e_2E0: mono_2Etyop_2Erealax_2Ereal] :
            ( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Eabs_2E1(V2e_2E0),mono_2Ec_2Ereal_2E_2F_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Ereal_2Epow_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2E_2B_2E2(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_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_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_2E0)),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_2E2(mono_2Ec_2Ereal_2E_2F_2E2(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_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),V2e_2E0)) ) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__sqrt__relative,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u] :
      ( ( p(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_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Enum_2E0_2E0) )
        & p(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_2E1(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))))))))))) )
     => ( p(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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0)))))))))
        & ? [V1e_2E0: mono_2Etyop_2Erealax_2Ereal] :
            ( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Eabs_2E1(V1e_2E0),mono_2Ec_2Ereal_2E_2F_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Ereal_2Epow_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2E_2B_2E2(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_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_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_2E0)),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0)))))))) = mono_2Ec_2Erealax_2Ereal__mul_2E2(mono_2Ec_2Etransc_2Esqrt_2E1(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_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),V1e_2E0)) ) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__mul__add__relative,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(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)))))
        & p(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_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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))))))))))) )
     => ( p(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_2E0)),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_2E0: mono_2Etyop_2Erealax_2Ereal] :
            ( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Eabs_2E1(V3e_2E0),mono_2Ec_2Ereal_2E_2F_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Ereal_2Epow_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2E_2B_2E2(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_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_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_2E0)),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_2E2(mono_2Ec_2Erealax_2Ereal__add_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),V3e_2E0)) ) ) ) ) ).

tff(thm_2Elift__ieee_2Efloat__mul__sub__relative,axiom,
    ! [A_27t: d,A_27w: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( p(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)))))
        & p(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)))))
        & p(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)))))
        & p(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_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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))))))))))) )
     => ( p(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_2E0)),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_2E0: mono_2Etyop_2Erealax_2Ereal] :
            ( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Eabs_2E1(V3e_2E0),mono_2Ec_2Ereal_2E_2F_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Ereal_2Epow_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2E_2B_2E2(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_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_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_2E0)),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_2E2(mono_2Ec_2Ereal_2Ereal__sub_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(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_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),V3e_2E0)) ) ) ) ) ).

tff(thm_2Elift__ieee_2Efinite__float__within__threshold,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( p(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)))))
     => ( ~ p(mono_2Ec_2Ereal_2Ereal__lte_2E2(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_2E1(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)))))))
        & ~ p(mono_2Ec_2Ereal_2Ereal__ge_2E2(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)))))) ) ) ).

tff(thm_2Elift__ieee_2Eround__finite__normal__float__id,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( p(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)))))
        & ~ p(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_2E0)),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) ) ) ).

tff(thm_2Elift__ieee_2Ereal__to__float__finite__normal__id,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( p(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)))))
        & ~ p(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_2E0)),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) ) ) ).

tff(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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0)))))))) = mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ) ).

tff(thm_2Elift__ieee_2Enon__representable__float__is__zero,axiom,
    ! [A_27a: d,A_27b: d,V0ff_2E0: mono_2Etyop_2Erealax_2Ereal,V1P_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Erealax_2Ereal__mul_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Ereal_2Eabs_2E1(V0ff_2E0)),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_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1P_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V0ff_2E0))))))) = mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ) ) ).

%------------------------------------------------------------------------------