ITP001 Axioms: ITP140+4.ax
%------------------------------------------------------------------------------
% File : ITP140+4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : lift_ieee.ax [Gau19]
% : HL4140+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 132 ( 72 unt; 0 def)
% Number of atoms : 292 ( 112 equ)
% Maximal formula atoms : 7 ( 2 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 predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 148 ( 148 usr; 79 con; 0-4 aty)
% Number of variables : 436 ( 425 !; 11 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).
fof(reserved_2Eho_2Ei__thm,axiom,
! [A_27a,V0x_2E0] : 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) ).
fof(reserved_2Eho_2Ek__thm,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] : 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) ).
fof(reserved_2Eho_2Es__thm,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : 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))))) ).
fof(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
& p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).
fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
=> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_3D,axiom,
! [A_27a,V0_2E0,V1_2E0] :
( p(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) ) ).
fof(reserved_2Equant_2E_21,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(reserved_2Equant_2E_3F,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
& p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
| p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
=> p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] :
( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
<=> p(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)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = 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))) ).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = 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))) ).
fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0] : 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))) = 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))) ).
fof(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,A_27b,X0_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)),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))) ).
fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
! [A_27t,A_27w,X0_2E0] : 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))) = 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))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0] : 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))) = 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))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__finite_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = 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))) ).
fof(arityeq3_2Ec_2Ebinary__ieee_2Eclosest__such_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_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),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0),s(tyop_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,X2_2E0))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__finite_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = 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))) ).
fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
! [A_27t,A_27w,X0_2E0] : 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))) ).
fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__sqrt_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0] : 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,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,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).
fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__add_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : 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,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,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).
fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__div_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : 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,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,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).
fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__mul_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : 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,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,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).
fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__sub_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : 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,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,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).
fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__add_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : 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,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,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))) ).
fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__sub_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : 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,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,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))) ).
fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_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,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__nan_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = 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))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__zero_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = 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))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = 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))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = 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))) ).
fof(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),c_2Ereal_2Ereal__of__num_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Ebinary__ieee_2Ereal__to__float_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Ereal__to__float_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_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,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_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,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = 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))) ).
fof(arityeq2_2Ec_2Ebinary__ieee_2Eround_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_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,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_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)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a,A_27b,X0_2E0,X1_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),X0_2E0),s(tyop_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,X1_2E0))) ).
fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Ewords_2EINT__MAX_2E1_2Emono_2EA_27w,axiom,
! [A_27w,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),X0_2E0))) = 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))) ).
fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : 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))) = 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))) ).
fof(arityeq2_2Ec_2Elift__ieee_2Eerror_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0] : 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,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(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))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__equal_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : 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))) = 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))) ).
fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__greater__equal_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : 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))) = 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))) ).
fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__greater__than_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : 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))) = 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))) ).
fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__less__equal_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : 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))) = 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))) ).
fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__less__than_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : 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))) = 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))) ).
fof(arityeq2_2Ec_2Elift__ieee_2Enormalizes_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0,X1_2E0] : 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,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq1_2Ec_2Etransc_2Esqrt_2E1,axiom,
! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Etransc_2Esqrt_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Etransc_2Esqrt_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).
fof(arityeq2_2Ec_2Ereal_2E_2F_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(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)),c_2Ereal_2E_2F_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(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)),c_2Erealax_2Ereal__add_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(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)),c_2Erealax_2Ereal__mul_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq2_2Ec_2Ereal_2Ereal__sub_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(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)),c_2Ereal_2Ereal__sub_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq2_2Ec_2Ereal_2Ereal__ge_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__ge_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ereal_2Ereal__ge_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Ethreshold_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = 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))) ).
fof(arityeq2_2Ec_2Ereal_2Ereal__gt_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__gt_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ereal_2Ereal__gt_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq1_2Ec_2Ereal_2Eabs_2E1,axiom,
! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2Eabs_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).
fof(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Erealax_2Ereal__lt_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Ethreshold_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = 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))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(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)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27t,axiom,
! [A_27t,X0_2E0] : s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),X0_2E0))) = 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))) ).
fof(arityeq2_2Ec_2Ereal_2Epow_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(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)),c_2Ereal_2Epow_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ereal_2Ereal__lte_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Elargest_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = 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))) ).
fof(arityeq1_2Ec_2Erealax_2Ereal__neg_2E1,axiom,
! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(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)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Erealax_2Einv_2E1,axiom,
! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Einv_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Einv_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = 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))) ).
fof(arityeq2_2Ec_2Ebinary__ieee_2Eround_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_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,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).
fof(arityeq3_2Ec_2Ebinary__ieee_2Eis__closest_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : 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,X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = 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,X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) ).
fof(thm_2Elift__ieee_2Eerror__def,axiom,
! [A_27t,A_27w,V0x_2E0] : 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,V0x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(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,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))))),s(tyop_2Erealax_2Ereal,V0x_2E0))) ).
fof(thm_2Elift__ieee_2Enormalizes__def,axiom,
! [A_27t,A_27w,V0x_2E0] :
( p(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,V0x_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Einv_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))),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)))))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__lt,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0)))) )
=> 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))) = s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0))))) ) ).
fof(thm_2Elift__ieee_2Efloat__le,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0)))) )
=> 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))) = s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0))))) ) ).
fof(thm_2Elift__ieee_2Efloat__gt,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0)))) )
=> 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))) = s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__gt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0))))) ) ).
fof(thm_2Elift__ieee_2Efloat__ge,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0)))) )
=> 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))) = s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__ge_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0))))) ) ).
fof(thm_2Elift__ieee_2Efloat__eq,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0)))) )
=> ( p(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))))
<=> s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1y_2E0))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__eq__refl,axiom,
! [A_27a,A_27b,V0x_2E0] :
( p(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(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) ) ).
fof(thm_2Elift__ieee_2Eis__closest__exits,axiom,
! [A_27a,A_27b,V0x_2E0,V1s_2E0] :
( p(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] : p(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,V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2a_2E0)))) ) ) ).
fof(thm_2Elift__ieee_2Eclosest__is__everything,axiom,
! [A_27a,A_27b,V0p_2E0,V1s_2E0,V2x_2E0] :
( p(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(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,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,V2x_2E0))))))
& ( ? [V3b_2E0] :
( p(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,V2x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V3b_2E0))))
& p(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(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,V2x_2E0)))))) ) ) ) ) ).
fof(thm_2Elift__ieee_2Eclosest__in__set,axiom,
! [A_27a,A_27b,V0p_2E0,V1s_2E0,V2x_2E0] :
( p(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(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,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0)))) ) ) ).
fof(thm_2Elift__ieee_2Eclosest__is__closest,axiom,
! [A_27a,A_27b,V0p_2E0,V1s_2E0,V2x_2E0] :
( p(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(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,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,V2x_2E0)))))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__finite,axiom,
! [A_27t,A_27w] : p(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)))) ).
fof(thm_2Elift__ieee_2Eis__finite__finite,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0a_2E0] : 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(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)))))) ) ).
fof(thm_2Elift__ieee_2Eis__finite__nonempty,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0a_2E0] : 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) ) ).
fof(thm_2Elift__ieee_2Eis__finite__closest,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V2a_2E0] : 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,V1x_2E0] : p(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,V1x_2E0)))))) ) ).
fof(thm_2Elift__ieee_2Efloat__to__real__finite,axiom,
! [A_27t,A_27w,V0x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))),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)))))) ) ).
fof(thm_2Elift__ieee_2Efloat__to__real__threshold,axiom,
! [A_27t,A_27w,V0x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))),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)))))) ) ).
fof(thm_2Elift__ieee_2Eerror__at__worst__lemma,axiom,
! [A_27t,A_27w,V0a_2E0,V1x_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0))),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(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(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,V1x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))) ) ).
fof(thm_2Elift__ieee_2Eerror__is__zero,axiom,
! [A_27t,A_27w,V0a_2E0,V1x_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))) = s(tyop_2Erealax_2Ereal,V1x_2E0) )
=> 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,V1x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ).
fof(thm_2Elift__ieee_2Erelative__error,axiom,
! [A_27t,A_27w,V0x_2E0] :
( p(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,V0x_2E0))))
=> ? [V1e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))
& 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,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V1e_2E0))))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__round__finite,axiom,
! [A_27t,A_27w,V0b_2E0,V1x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0))),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(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,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0)))))) ) ).
fof(thm_2Elift__ieee_2Efloat__add,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))),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(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,c_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_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,c_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_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),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,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__sub,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))),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(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,c_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_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,c_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_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),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,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__mul,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))),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(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,c_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_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,c_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_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),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,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__div,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))),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(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,c_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_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,c_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_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),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,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__sqrt,axiom,
! [A_27t,A_27w,V0a_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& 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))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Etransc_2Esqrt_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))))),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(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,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))))))
& 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,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Etransc_2Esqrt_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))),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,c_2Etransc_2Esqrt_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))))))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__mul__add,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0,V2c_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))))),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(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,c_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))))))))
& 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,c_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))))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))),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,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))))))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__mul__sub,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0,V2c_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))))),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(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,c_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))))))))
& 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,c_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))))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))),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,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))))))) ) ) ).
fof(thm_2Elift__ieee_2Efloat__add__finite,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))),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(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,c_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)))))))) ) ).
fof(thm_2Elift__ieee_2Efloat__sub__finite,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))),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(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,c_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)))))))) ) ).
fof(thm_2Elift__ieee_2Efloat__mul__finite,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))),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(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,c_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)))))))) ) ).
fof(thm_2Elift__ieee_2Efloat__div__finite,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))),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(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,c_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)))))))) ) ).
fof(thm_2Elift__ieee_2Efloat__sqrt__finite,axiom,
! [A_27t,A_27w,V0a_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& 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))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Etransc_2Esqrt_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))))),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(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,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0)))))))) ) ).
fof(thm_2Elift__ieee_2Efloat__mul__add__finite,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0,V2c_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))))),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(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,c_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)))))))) ) ).
fof(thm_2Elift__ieee_2Efloat__mul__sub__finite,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0,V2c_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))))),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(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,c_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)))))))) ) ).
fof(thm_2Elift__ieee_2Efloat__add__relative,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(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,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0)))))))) )
=> ( p(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,c_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] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))
& 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,c_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_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V2e_2E0))))) ) ) ) ).
fof(thm_2Elift__ieee_2Efloat__sub__relative,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(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,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0)))))))) )
=> ( p(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,c_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] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))
& 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,c_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_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V2e_2E0))))) ) ) ) ).
fof(thm_2Elift__ieee_2Efloat__mul__relative,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(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,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0)))))))) )
=> ( p(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,c_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] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))
& 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,c_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_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V2e_2E0))))) ) ) ) ).
fof(thm_2Elift__ieee_2Efloat__div__relative,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(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,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0)))))))) )
=> ( p(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,c_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] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))
& 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,c_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_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V2e_2E0))))) ) ) ) ).
fof(thm_2Elift__ieee_2Efloat__sqrt__relative,axiom,
! [A_27t,A_27w,V0a_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& 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))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
& p(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,c_2Etransc_2Esqrt_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0)))))))) )
=> ( p(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,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))))))
& ? [V1e_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))
& 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,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Etransc_2Esqrt_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V1e_2E0))))) ) ) ) ).
fof(thm_2Elift__ieee_2Efloat__mul__add__relative,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0,V2c_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))
& p(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,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0)))))))) )
=> ( p(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,c_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] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V3e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))
& 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,c_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))))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V3e_2E0))))) ) ) ) ).
fof(thm_2Elift__ieee_2Efloat__mul__sub__relative,axiom,
! [A_27t,A_27w,V0a_2E0,V1b_2E0,V2c_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))
& p(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,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0)))))))) )
=> ( p(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,c_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] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V3e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))
& 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,c_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))))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V3e_2E0))))) ) ) ) ).
fof(thm_2Elift__ieee_2Efinite__float__within__threshold,axiom,
! [A_27a,A_27b,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0f_2E0))))
=> ( ~ p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0f_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(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(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__ge_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0f_2E0))),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)))))) ) ) ).
fof(thm_2Elift__ieee_2Eround__finite__normal__float__id,axiom,
! [A_27a,A_27b,V0f_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0f_2E0))))
& ~ p(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,c_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) ) ).
fof(thm_2Elift__ieee_2Ereal__to__float__finite__normal__id,axiom,
! [A_27a,A_27b,V0f_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0f_2E0))))
& ~ p(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,c_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) ) ).
fof(thm_2Elift__ieee_2Efloat__to__real__real__to__float__zero__id,axiom,
! [A_27a,A_27b] : 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,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ).
fof(thm_2Elift__ieee_2Enon__representable__float__is__zero,axiom,
! [A_27a,A_27b,V0ff_2E0,V1P_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0ff_2E0))))),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))))))
=> 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,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Emin_2Ebool,V1P_2E0),s(tyop_2Erealax_2Ereal,V0ff_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ).
fof(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
( ! [V2x_2E0] : 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) ) ).
%------------------------------------------------------------------------------