%------------------------------------------------------------------------------
% File     : ITP021+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Problem  : HOL4 set theory export of thm_2Eextreal_2Emax__le.p, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : thm_2Eextreal_2Emax__le.p [Gau20]
%          : HL410001+5.p [TPAP]

% Status   : Theorem
% Rating   : 0.89 v8.2.0, 0.94 v7.5.0
% Syntax   : Number of formulae    : 19039 (1861 unt;   0 def)
%            Number of atoms       : 119337 (20626 equ)
%            Maximal formula atoms : 5765 (   6 avg)
%            Number of connectives : 102825 (2527   ~;1056   |;26643   &)
%                                         (6165 <=>;66434  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  363 (   8 avg)
%            Maximal term depth    :  130 (   2 avg)
%            Number of predicates  :    6 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    : 5762 (5762 usr;1163 con; 0-11 aty)
%            Number of variables   : 79604 (65705   !;13899   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001+2.ax').
include('Axioms/ITP001/ITP002+5.ax').
include('Axioms/ITP001/ITP003+5.ax').
include('Axioms/ITP001/ITP004+5.ax').
include('Axioms/ITP001/ITP007+5.ax').
include('Axioms/ITP001/ITP006+5.ax').
include('Axioms/ITP001/ITP005+5.ax').
include('Axioms/ITP001/ITP008+5.ax').
include('Axioms/ITP001/ITP009+5.ax').
include('Axioms/ITP001/ITP010+5.ax').
include('Axioms/ITP001/ITP012+5.ax').
include('Axioms/ITP001/ITP011+5.ax').
include('Axioms/ITP001/ITP013+5.ax').
include('Axioms/ITP001/ITP014+5.ax').
include('Axioms/ITP001/ITP015+5.ax').
include('Axioms/ITP001/ITP017+5.ax').
include('Axioms/ITP001/ITP016+5.ax').
include('Axioms/ITP001/ITP019+5.ax').
include('Axioms/ITP001/ITP018+5.ax').
include('Axioms/ITP001/ITP021+5.ax').
include('Axioms/ITP001/ITP022+5.ax').
include('Axioms/ITP001/ITP020+5.ax').
include('Axioms/ITP001/ITP024+5.ax').
include('Axioms/ITP001/ITP023+5.ax').
include('Axioms/ITP001/ITP025+5.ax').
include('Axioms/ITP001/ITP026+5.ax').
include('Axioms/ITP001/ITP027+5.ax').
include('Axioms/ITP001/ITP028+5.ax').
include('Axioms/ITP001/ITP031+5.ax').
include('Axioms/ITP001/ITP029+5.ax').
include('Axioms/ITP001/ITP033+5.ax').
include('Axioms/ITP001/ITP030+5.ax').
include('Axioms/ITP001/ITP032+5.ax').
include('Axioms/ITP001/ITP038+5.ax').
include('Axioms/ITP001/ITP035+5.ax').
include('Axioms/ITP001/ITP034+5.ax').
include('Axioms/ITP001/ITP036+5.ax').
include('Axioms/ITP001/ITP037+5.ax').
include('Axioms/ITP001/ITP039+5.ax').
include('Axioms/ITP001/ITP041+5.ax').
include('Axioms/ITP001/ITP042+5.ax').
include('Axioms/ITP001/ITP040+5.ax').
include('Axioms/ITP001/ITP044+5.ax').
include('Axioms/ITP001/ITP051+5.ax').
include('Axioms/ITP001/ITP045+5.ax').
include('Axioms/ITP001/ITP056+5.ax').
include('Axioms/ITP001/ITP046+5.ax').
include('Axioms/ITP001/ITP043+5.ax').
include('Axioms/ITP001/ITP052+5.ax').
include('Axioms/ITP001/ITP057+5.ax').
include('Axioms/ITP001/ITP048+5.ax').
include('Axioms/ITP001/ITP047+5.ax').
include('Axioms/ITP001/ITP055+5.ax').
include('Axioms/ITP001/ITP053+5.ax').
include('Axioms/ITP001/ITP054+5.ax').
include('Axioms/ITP001/ITP058+5.ax').
include('Axioms/ITP001/ITP049+5.ax').
include('Axioms/ITP001/ITP050+5.ax').
include('Axioms/ITP001/ITP061+5.ax').
include('Axioms/ITP001/ITP069+5.ax').
include('Axioms/ITP001/ITP062+5.ax').
include('Axioms/ITP001/ITP068+5.ax').
include('Axioms/ITP001/ITP078+5.ax').
include('Axioms/ITP001/ITP064+5.ax').
include('Axioms/ITP001/ITP060+5.ax').
include('Axioms/ITP001/ITP067+5.ax').
include('Axioms/ITP001/ITP075+5.ax').
include('Axioms/ITP001/ITP074+5.ax').
include('Axioms/ITP001/ITP063+5.ax').
include('Axioms/ITP001/ITP059+5.ax').
include('Axioms/ITP001/ITP065+5.ax').
include('Axioms/ITP001/ITP076+5.ax').
include('Axioms/ITP001/ITP066+5.ax').
include('Axioms/ITP001/ITP077+5.ax').
include('Axioms/ITP001/ITP070+5.ax').
include('Axioms/ITP001/ITP071+5.ax').
include('Axioms/ITP001/ITP072+5.ax').
include('Axioms/ITP001/ITP073+5.ax').
include('Axioms/ITP001/ITP080+5.ax').
include('Axioms/ITP001/ITP083+5.ax').
include('Axioms/ITP001/ITP088+5.ax').
include('Axioms/ITP001/ITP082+5.ax').
include('Axioms/ITP001/ITP081+5.ax').
include('Axioms/ITP001/ITP079+5.ax').
include('Axioms/ITP001/ITP087+5.ax').
include('Axioms/ITP001/ITP085+5.ax').
include('Axioms/ITP001/ITP086+5.ax').
include('Axioms/ITP001/ITP090+5.ax').
include('Axioms/ITP001/ITP089+5.ax').
include('Axioms/ITP001/ITP084+5.ax').
include('Axioms/ITP001/ITP104+5.ax').
include('Axioms/ITP001/ITP097+5.ax').
include('Axioms/ITP001/ITP094+5.ax').
include('Axioms/ITP001/ITP095+5.ax').
include('Axioms/ITP001/ITP093+5.ax').
include('Axioms/ITP001/ITP102+5.ax').
include('Axioms/ITP001/ITP091+5.ax').
include('Axioms/ITP001/ITP098+5.ax').
include('Axioms/ITP001/ITP096+5.ax').
include('Axioms/ITP001/ITP100+5.ax').
include('Axioms/ITP001/ITP092+5.ax').
include('Axioms/ITP001/ITP105+5.ax').
include('Axioms/ITP001/ITP101+5.ax').
include('Axioms/ITP001/ITP103+5.ax').
include('Axioms/ITP001/ITP099+5.ax').
include('Axioms/ITP001/ITP111+5.ax').
include('Axioms/ITP001/ITP108+5.ax').
include('Axioms/ITP001/ITP106+5.ax').
include('Axioms/ITP001/ITP107+5.ax').
include('Axioms/ITP001/ITP114+5.ax').
include('Axioms/ITP001/ITP110+5.ax').
include('Axioms/ITP001/ITP109+5.ax').
include('Axioms/ITP001/ITP112+5.ax').
include('Axioms/ITP001/ITP113+5.ax').
include('Axioms/ITP001/ITP117+5.ax').
include('Axioms/ITP001/ITP116+5.ax').
include('Axioms/ITP001/ITP118+5.ax').
include('Axioms/ITP001/ITP120+5.ax').
include('Axioms/ITP001/ITP119+5.ax').
include('Axioms/ITP001/ITP121+5.ax').
include('Axioms/ITP001/ITP123+5.ax').
include('Axioms/ITP001/ITP124+5.ax').
include('Axioms/ITP001/ITP126+5.ax').
include('Axioms/ITP001/ITP127+5.ax').
include('Axioms/ITP001/ITP129+5.ax').
include('Axioms/ITP001/ITP128+5.ax').
include('Axioms/ITP001/ITP130+5.ax').
include('Axioms/ITP001/ITP131+5.ax').
include('Axioms/ITP001/ITP132+5.ax').
include('Axioms/ITP001/ITP134+5.ax').
include('Axioms/ITP001/ITP133+5.ax').
include('Axioms/ITP001/ITP135+5.ax').
include('Axioms/ITP001/ITP136+5.ax').
include('Axioms/ITP001/ITP138+5.ax').
include('Axioms/ITP001/ITP137+5.ax').
include('Axioms/ITP001/ITP140+5.ax').
include('Axioms/ITP001/ITP141+5.ax').
include('Axioms/ITP001/ITP139+5.ax').
include('Axioms/ITP001/ITP142+5.ax').
include('Axioms/ITP001/ITP145+5.ax').
include('Axioms/ITP001/ITP144+5.ax').
%------------------------------------------------------------------------------
fof(ne_ty_2Eextreal_2Eextreal,axiom,
    ne(ty_2Eextreal_2Eextreal) ).

fof(mem_c_2Eextreal_2EEXTREAL__SUM__IMAGE,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => mem(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),arr(arr(A_27a,ty_2Eextreal_2Eextreal),arr(arr(A_27a,bool),ty_2Eextreal_2Eextreal))) ) ).

fof(mem_c_2Eextreal_2ENegInf,axiom,
    mem(c_2Eextreal_2ENegInf,ty_2Eextreal_2Eextreal) ).

fof(mem_c_2Eextreal_2ENormal,axiom,
    mem(c_2Eextreal_2ENormal,arr(ty_2Erealax_2Ereal,ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2EPosInf,axiom,
    mem(c_2Eextreal_2EPosInf,ty_2Eextreal_2Eextreal) ).

fof(mem_c_2Eextreal_2EQ__set,axiom,
    mem(c_2Eextreal_2EQ__set,arr(ty_2Eextreal_2Eextreal,bool)) ).

fof(mem_c_2Eextreal_2Eceiling,axiom,
    mem(c_2Eextreal_2Eceiling,arr(ty_2Eextreal_2Eextreal,ty_2Enum_2Enum)) ).

fof(mem_c_2Eextreal_2Eext__mono__decreasing,axiom,
    mem(c_2Eextreal_2Eext__mono__decreasing,arr(arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),bool)) ).

fof(mem_c_2Eextreal_2Eext__mono__increasing,axiom,
    mem(c_2Eextreal_2Eext__mono__increasing,arr(arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),bool)) ).

fof(mem_c_2Eextreal_2Eext__suminf,axiom,
    mem(c_2Eextreal_2Eext__suminf,arr(arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2Eextreal__CASE,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => mem(c_2Eextreal_2Eextreal__CASE(A_27a),arr(ty_2Eextreal_2Eextreal,arr(A_27a,arr(A_27a,arr(arr(ty_2Erealax_2Ereal,A_27a),A_27a))))) ) ).

fof(mem_c_2Eextreal_2Eextreal__abs,axiom,
    mem(c_2Eextreal_2Eextreal__abs,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2Eextreal__add,axiom,
    mem(c_2Eextreal_2Eextreal__add,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))) ).

fof(mem_c_2Eextreal_2Eextreal__ainv,axiom,
    mem(c_2Eextreal_2Eextreal__ainv,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2Eextreal__div,axiom,
    mem(c_2Eextreal_2Eextreal__div,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))) ).

fof(mem_c_2Eextreal_2Eextreal__exp,axiom,
    mem(c_2Eextreal_2Eextreal__exp,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2Eextreal__inf,axiom,
    mem(c_2Eextreal_2Eextreal__inf,arr(arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2Eextreal__inv,axiom,
    mem(c_2Eextreal_2Eextreal__inv,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2Eextreal__le,axiom,
    mem(c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ).

fof(mem_c_2Eextreal_2Eextreal__lg,axiom,
    mem(c_2Eextreal_2Eextreal__lg,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2Eextreal__logr,axiom,
    mem(c_2Eextreal_2Eextreal__logr,arr(ty_2Erealax_2Ereal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))) ).

fof(mem_c_2Eextreal_2Eextreal__lt,axiom,
    mem(c_2Eextreal_2Eextreal__lt,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ).

fof(mem_c_2Eextreal_2Eextreal__max,axiom,
    mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))) ).

fof(mem_c_2Eextreal_2Eextreal__min,axiom,
    mem(c_2Eextreal_2Eextreal__min,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))) ).

fof(mem_c_2Eextreal_2Eextreal__mul,axiom,
    mem(c_2Eextreal_2Eextreal__mul,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))) ).

fof(mem_c_2Eextreal_2Eextreal__of__num,axiom,
    mem(c_2Eextreal_2Eextreal__of__num,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2Eextreal__pow,axiom,
    mem(c_2Eextreal_2Eextreal__pow,arr(ty_2Eextreal_2Eextreal,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))) ).

fof(mem_c_2Eextreal_2Eextreal__size,axiom,
    mem(c_2Eextreal_2Eextreal__size,arr(ty_2Eextreal_2Eextreal,ty_2Enum_2Enum)) ).

fof(mem_c_2Eextreal_2Eextreal__sqrt,axiom,
    mem(c_2Eextreal_2Eextreal__sqrt,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2Eextreal__sub,axiom,
    mem(c_2Eextreal_2Eextreal__sub,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))) ).

fof(mem_c_2Eextreal_2Eextreal__sup,axiom,
    mem(c_2Eextreal_2Eextreal__sup,arr(arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) ).

fof(mem_c_2Eextreal_2Emono__decreasing,axiom,
    mem(c_2Eextreal_2Emono__decreasing,arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),bool)) ).

fof(mem_c_2Eextreal_2Emono__increasing,axiom,
    mem(c_2Eextreal_2Emono__increasing,arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),bool)) ).

fof(mem_c_2Eextreal_2Eopen__interval,axiom,
    mem(c_2Eextreal_2Eopen__interval,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool)))) ).

fof(mem_c_2Eextreal_2Eopen__intervals__set,axiom,
    mem(c_2Eextreal_2Eopen__intervals__set,arr(arr(ty_2Eextreal_2Eextreal,bool),bool)) ).

fof(mem_c_2Eextreal_2Erational__intervals,axiom,
    mem(c_2Eextreal_2Erational__intervals,arr(arr(ty_2Eextreal_2Eextreal,bool),bool)) ).

fof(mem_c_2Eextreal_2Ereal,axiom,
    mem(c_2Eextreal_2Ereal,arr(ty_2Eextreal_2Eextreal,ty_2Erealax_2Ereal)) ).

fof(lameq_f3341,axiom,
    ! [V7a] : ap(f3341,V7a) = ap(ap(ap(c_2Eind__type_2ECONSTR(ty_2Erealax_2Ereal),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0))),V7a),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(ty_2Erealax_2Ereal))) ).

fof(lameq_f3342,axiom,
    ! [V3a0] :
      ( mem(V3a0,ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal))
     => ! [V6a] : ap(f3342(V3a0),V6a) = ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal)),V3a0),ap(f3341,V6a)) ) ).

fof(lameq_f3343,axiom,
    ! [V2_27extreal_27] :
      ( mem(V2_27extreal_27,arr(ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal),bool))
     => ! [V3a0] : ap(f3343(V2_27extreal_27),V3a0) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal)),V3a0),ap(ap(ap(c_2Eind__type_2ECONSTR(ty_2Erealax_2Ereal),c_2Enum_2E0),c_2Ebool_2EARB(ty_2Erealax_2Ereal)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(ty_2Erealax_2Ereal))))),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal)),V3a0),ap(ap(ap(c_2Eind__type_2ECONSTR(ty_2Erealax_2Ereal),ap(c_2Enum_2ESUC,c_2Enum_2E0)),c_2Ebool_2EARB(ty_2Erealax_2Ereal)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(ty_2Erealax_2Ereal))))),ap(c_2Ebool_2E_3F(ty_2Erealax_2Ereal),f3342(V3a0))))),ap(V2_27extreal_27,V3a0)) ) ).

fof(lameq_f3344,axiom,
    ! [V1a0] :
      ( mem(V1a0,ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal))
     => ! [V2_27extreal_27] : ap(f3344(V1a0),V2_27extreal_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal)),f3343(V2_27extreal_27))),ap(V2_27extreal_27,V1a0)) ) ).

fof(lameq_f3345,axiom,
    ! [V1a0] : ap(f3345,V1a0) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal),bool)),f3344(V1a0)) ).

fof(ax_thm_2Eextreal_2Eextreal__TY__DEF,axiom,
    ? [V0rep] :
      ( mem(V0rep,arr(ty_2Eextreal_2Eextreal,ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal)))
      & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal),ty_2Eextreal_2Eextreal),f3345),V0rep)) ) ).

fof(ax_thm_2Eextreal_2Eextreal__case__def,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ( ! [V0v] :
            ( mem(V0v,A_27a)
           => ! [V1v1] :
                ( mem(V1v1,A_27a)
               => ! [V2f] :
                    ( mem(V2f,arr(ty_2Erealax_2Ereal,A_27a))
                   => ap(ap(ap(ap(c_2Eextreal_2Eextreal__CASE(A_27a),c_2Eextreal_2ENegInf),V0v),V1v1),V2f) = V0v ) ) )
        & ! [V3v] :
            ( mem(V3v,A_27a)
           => ! [V4v1] :
                ( mem(V4v1,A_27a)
               => ! [V5f] :
                    ( mem(V5f,arr(ty_2Erealax_2Ereal,A_27a))
                   => ap(ap(ap(ap(c_2Eextreal_2Eextreal__CASE(A_27a),c_2Eextreal_2EPosInf),V3v),V4v1),V5f) = V4v1 ) ) )
        & ! [V6a] :
            ( mem(V6a,ty_2Erealax_2Ereal)
           => ! [V7v] :
                ( mem(V7v,A_27a)
               => ! [V8v1] :
                    ( mem(V8v1,A_27a)
                   => ! [V9f] :
                        ( mem(V9f,arr(ty_2Erealax_2Ereal,A_27a))
                       => ap(ap(ap(ap(c_2Eextreal_2Eextreal__CASE(A_27a),ap(c_2Eextreal_2ENormal,V6a)),V7v),V8v1),V9f) = ap(V9f,V6a) ) ) ) ) ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__size__def,axiom,
    ( ap(c_2Eextreal_2Eextreal__size,c_2Eextreal_2ENegInf) = c_2Enum_2E0
    & ap(c_2Eextreal_2Eextreal__size,c_2Eextreal_2EPosInf) = c_2Enum_2E0
    & ! [V0a] :
        ( mem(V0a,ty_2Erealax_2Ereal)
       => ap(c_2Eextreal_2Eextreal__size,ap(c_2Eextreal_2ENormal,V0a)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ).

fof(conj_thm_2Eextreal_2Edatatype__extreal,axiom,
    ! [V0extreal] :
      ( mem(V0extreal,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,arr(arr(ty_2Erealax_2Ereal,ty_2Eextreal_2Eextreal),bool))))
     => p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(V0extreal,c_2Eextreal_2ENegInf),c_2Eextreal_2EPosInf),c_2Eextreal_2ENormal))) ) ).

fof(conj_thm_2Eextreal_2Eextreal__distinct,axiom,
    ( c_2Eextreal_2ENegInf != c_2Eextreal_2EPosInf
    & ! [V0a] :
        ( mem(V0a,ty_2Erealax_2Ereal)
       => c_2Eextreal_2ENegInf != ap(c_2Eextreal_2ENormal,V0a) )
    & ! [V1a] :
        ( mem(V1a,ty_2Erealax_2Ereal)
       => c_2Eextreal_2EPosInf != ap(c_2Eextreal_2ENormal,V1a) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__nchotomy,axiom,
    ! [V0ee] :
      ( mem(V0ee,ty_2Eextreal_2Eextreal)
     => ( V0ee = c_2Eextreal_2ENegInf
        | V0ee = c_2Eextreal_2EPosInf
        | ? [V1r] :
            ( mem(V1r,ty_2Erealax_2Ereal)
            & V0ee = ap(c_2Eextreal_2ENormal,V1r) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__Axiom,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f0] :
          ( mem(V0f0,A_27a)
         => ! [V1f1] :
              ( mem(V1f1,A_27a)
             => ! [V2f2] :
                  ( mem(V2f2,arr(ty_2Erealax_2Ereal,A_27a))
                 => ? [V3fn] :
                      ( mem(V3fn,arr(ty_2Eextreal_2Eextreal,A_27a))
                      & ap(V3fn,c_2Eextreal_2ENegInf) = V0f0
                      & ap(V3fn,c_2Eextreal_2EPosInf) = V1f1
                      & ! [V4a] :
                          ( mem(V4a,ty_2Erealax_2Ereal)
                         => ap(V3fn,ap(c_2Eextreal_2ENormal,V4a)) = ap(V2f2,V4a) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__induction,axiom,
    ! [V0P] :
      ( mem(V0P,arr(ty_2Eextreal_2Eextreal,bool))
     => ( ( p(ap(V0P,c_2Eextreal_2ENegInf))
          & p(ap(V0P,c_2Eextreal_2EPosInf))
          & ! [V1r] :
              ( mem(V1r,ty_2Erealax_2Ereal)
             => p(ap(V0P,ap(c_2Eextreal_2ENormal,V1r))) ) )
       => ! [V2e] :
            ( mem(V2e,ty_2Eextreal_2Eextreal)
           => p(ap(V0P,V2e)) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__case__cong,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0v_27] :
          ( mem(V0v_27,A_27a)
         => ! [V1v1_27] :
              ( mem(V1v1_27,A_27a)
             => ! [V2f_27] :
                  ( mem(V2f_27,arr(ty_2Erealax_2Ereal,A_27a))
                 => ! [V3M] :
                      ( mem(V3M,ty_2Eextreal_2Eextreal)
                     => ! [V4M_27] :
                          ( mem(V4M_27,ty_2Eextreal_2Eextreal)
                         => ! [V5v] :
                              ( mem(V5v,A_27a)
                             => ! [V6v1] :
                                  ( mem(V6v1,A_27a)
                                 => ! [V7f] :
                                      ( mem(V7f,arr(ty_2Erealax_2Ereal,A_27a))
                                     => ( ( V3M = V4M_27
                                          & ( V4M_27 = c_2Eextreal_2ENegInf
                                           => V5v = V0v_27 )
                                          & ( V4M_27 = c_2Eextreal_2EPosInf
                                           => V6v1 = V1v1_27 )
                                          & ! [V8a] :
                                              ( mem(V8a,ty_2Erealax_2Ereal)
                                             => ( V4M_27 = ap(c_2Eextreal_2ENormal,V8a)
                                               => ap(V7f,V8a) = ap(V2f_27,V8a) ) ) )
                                       => ap(ap(ap(ap(c_2Eextreal_2Eextreal__CASE(A_27a),V3M),V5v),V6v1),V7f) = ap(ap(ap(ap(c_2Eextreal_2Eextreal__CASE(A_27a),V4M_27),V0v_27),V1v1_27),V2f_27) ) ) ) ) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__case__eq,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0x] :
          ( mem(V0x,ty_2Eextreal_2Eextreal)
         => ! [V1v] :
              ( mem(V1v,A_27a)
             => ! [V2v1] :
                  ( mem(V2v1,A_27a)
                 => ! [V3f] :
                      ( mem(V3f,arr(ty_2Erealax_2Ereal,A_27a))
                     => ! [V4v_27] :
                          ( mem(V4v_27,A_27a)
                         => ( ap(ap(ap(ap(c_2Eextreal_2Eextreal__CASE(A_27a),V0x),V1v),V2v1),V3f) = V4v_27
                          <=> ( ( V0x = c_2Eextreal_2ENegInf
                                & V1v = V4v_27 )
                              | ( V0x = c_2Eextreal_2EPosInf
                                & V2v1 = V4v_27 )
                              | ? [V5r] :
                                  ( mem(V5r,ty_2Erealax_2Ereal)
                                  & V0x = ap(c_2Eextreal_2ENormal,V5r)
                                  & ap(V3f,V5r) = V4v_27 ) ) ) ) ) ) ) ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__of__num__def,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ap(c_2Eextreal_2Eextreal__of__num,V0n) = ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,V0n)) ) ).

fof(lameq_f3346,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1r] : ap(f3346(V0x),V1r) = ap(ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),V0x),ap(c_2Eextreal_2ENormal,V1r)) ) ).

fof(ax_thm_2Eextreal_2Ereal__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(c_2Eextreal_2Ereal,V0x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),V0x),c_2Eextreal_2ENegInf)),ap(ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),V0x),c_2Eextreal_2EPosInf))),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Emin_2E_40(ty_2Erealax_2Ereal),f3346(V0x))) ) ).

fof(conj_thm_2Eextreal_2Ereal__normal,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ap(c_2Eextreal_2Ereal,ap(c_2Eextreal_2ENormal,V0x)) = V0x ) ).

fof(conj_thm_2Eextreal_2Enormal__real,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( ( V0x != c_2Eextreal_2ENegInf
          & V0x != c_2Eextreal_2EPosInf )
       => ap(c_2Eextreal_2ENormal,ap(c_2Eextreal_2Ereal,V0x)) = V0x ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__add__ind,axiom,
    ! [V0P] :
      ( mem(V0P,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool)))
     => ( ( ! [V1x] :
              ( mem(V1x,ty_2Erealax_2Ereal)
             => ! [V2y] :
                  ( mem(V2y,ty_2Erealax_2Ereal)
                 => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V1x)),ap(c_2Eextreal_2ENormal,V2y))) ) )
          & ! [V3a] :
              ( mem(V3a,ty_2Eextreal_2Eextreal)
             => p(ap(ap(V0P,c_2Eextreal_2EPosInf),V3a)) )
          & p(ap(ap(V0P,c_2Eextreal_2ENegInf),c_2Eextreal_2EPosInf))
          & ! [V4v2] :
              ( mem(V4v2,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V4v2)),c_2Eextreal_2EPosInf)) )
          & p(ap(ap(V0P,c_2Eextreal_2ENegInf),c_2Eextreal_2ENegInf))
          & ! [V5v5] :
              ( mem(V5v5,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,c_2Eextreal_2ENegInf),ap(c_2Eextreal_2ENormal,V5v5))) )
          & ! [V6v3] :
              ( mem(V6v3,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V6v3)),c_2Eextreal_2ENegInf)) ) )
       => ! [V7v] :
            ( mem(V7v,ty_2Eextreal_2Eextreal)
           => ! [V8v1] :
                ( mem(V8v1,ty_2Eextreal_2Eextreal)
               => p(ap(ap(V0P,V7v),V8v1)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__add__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ! [V2a] :
              ( mem(V2a,ty_2Eextreal_2Eextreal)
             => ! [V3v2] :
                  ( mem(V3v2,ty_2Erealax_2Ereal)
                 => ! [V4v5] :
                      ( mem(V4v5,ty_2Erealax_2Ereal)
                     => ! [V5v3] :
                          ( mem(V5v3,ty_2Erealax_2Ereal)
                         => ( ap(ap(c_2Eextreal_2Eextreal__add,ap(c_2Eextreal_2ENormal,V0x)),ap(c_2Eextreal_2ENormal,V1y)) = ap(c_2Eextreal_2ENormal,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))
                            & ap(ap(c_2Eextreal_2Eextreal__add,c_2Eextreal_2EPosInf),V2a) = c_2Eextreal_2EPosInf
                            & ap(ap(c_2Eextreal_2Eextreal__add,c_2Eextreal_2ENegInf),c_2Eextreal_2EPosInf) = c_2Eextreal_2EPosInf
                            & ap(ap(c_2Eextreal_2Eextreal__add,ap(c_2Eextreal_2ENormal,V3v2)),c_2Eextreal_2EPosInf) = c_2Eextreal_2EPosInf
                            & ap(ap(c_2Eextreal_2Eextreal__add,c_2Eextreal_2ENegInf),c_2Eextreal_2ENegInf) = c_2Eextreal_2ENegInf
                            & ap(ap(c_2Eextreal_2Eextreal__add,c_2Eextreal_2ENegInf),ap(c_2Eextreal_2ENormal,V4v5)) = c_2Eextreal_2ENegInf
                            & ap(ap(c_2Eextreal_2Eextreal__add,ap(c_2Eextreal_2ENormal,V5v3)),c_2Eextreal_2ENegInf) = c_2Eextreal_2ENegInf ) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__sub__ind,axiom,
    ! [V0P] :
      ( mem(V0P,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool)))
     => ( ( ! [V1x] :
              ( mem(V1x,ty_2Erealax_2Ereal)
             => ! [V2y] :
                  ( mem(V2y,ty_2Erealax_2Ereal)
                 => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V1x)),ap(c_2Eextreal_2ENormal,V2y))) ) )
          & ! [V3a] :
              ( mem(V3a,ty_2Eextreal_2Eextreal)
             => p(ap(ap(V0P,c_2Eextreal_2EPosInf),V3a)) )
          & p(ap(ap(V0P,c_2Eextreal_2ENegInf),c_2Eextreal_2EPosInf))
          & ! [V4v2] :
              ( mem(V4v2,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V4v2)),c_2Eextreal_2EPosInf)) )
          & p(ap(ap(V0P,c_2Eextreal_2ENegInf),c_2Eextreal_2ENegInf))
          & ! [V5v5] :
              ( mem(V5v5,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,c_2Eextreal_2ENegInf),ap(c_2Eextreal_2ENormal,V5v5))) )
          & ! [V6v3] :
              ( mem(V6v3,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V6v3)),c_2Eextreal_2ENegInf)) ) )
       => ! [V7v] :
            ( mem(V7v,ty_2Eextreal_2Eextreal)
           => ! [V8v1] :
                ( mem(V8v1,ty_2Eextreal_2Eextreal)
               => p(ap(ap(V0P,V7v),V8v1)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__sub__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ! [V2a] :
              ( mem(V2a,ty_2Eextreal_2Eextreal)
             => ! [V3v2] :
                  ( mem(V3v2,ty_2Erealax_2Ereal)
                 => ! [V4v5] :
                      ( mem(V4v5,ty_2Erealax_2Ereal)
                     => ! [V5v3] :
                          ( mem(V5v3,ty_2Erealax_2Ereal)
                         => ( ap(ap(c_2Eextreal_2Eextreal__sub,ap(c_2Eextreal_2ENormal,V0x)),ap(c_2Eextreal_2ENormal,V1y)) = ap(c_2Eextreal_2ENormal,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y))
                            & ap(ap(c_2Eextreal_2Eextreal__sub,c_2Eextreal_2EPosInf),V2a) = c_2Eextreal_2EPosInf
                            & ap(ap(c_2Eextreal_2Eextreal__sub,c_2Eextreal_2ENegInf),c_2Eextreal_2EPosInf) = c_2Eextreal_2ENegInf
                            & ap(ap(c_2Eextreal_2Eextreal__sub,ap(c_2Eextreal_2ENormal,V3v2)),c_2Eextreal_2EPosInf) = c_2Eextreal_2ENegInf
                            & ap(ap(c_2Eextreal_2Eextreal__sub,c_2Eextreal_2ENegInf),c_2Eextreal_2ENegInf) = c_2Eextreal_2EPosInf
                            & ap(ap(c_2Eextreal_2Eextreal__sub,c_2Eextreal_2ENegInf),ap(c_2Eextreal_2ENormal,V4v5)) = c_2Eextreal_2ENegInf
                            & ap(ap(c_2Eextreal_2Eextreal__sub,ap(c_2Eextreal_2ENormal,V5v3)),c_2Eextreal_2ENegInf) = c_2Eextreal_2EPosInf ) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__le__ind,axiom,
    ! [V0P] :
      ( mem(V0P,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool)))
     => ( ( ! [V1x] :
              ( mem(V1x,ty_2Erealax_2Ereal)
             => ! [V2y] :
                  ( mem(V2y,ty_2Erealax_2Ereal)
                 => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V1x)),ap(c_2Eextreal_2ENormal,V2y))) ) )
          & ! [V3a] :
              ( mem(V3a,ty_2Eextreal_2Eextreal)
             => p(ap(ap(V0P,c_2Eextreal_2ENegInf),V3a)) )
          & p(ap(ap(V0P,c_2Eextreal_2EPosInf),c_2Eextreal_2EPosInf))
          & ! [V4v2] :
              ( mem(V4v2,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V4v2)),c_2Eextreal_2EPosInf)) )
          & p(ap(ap(V0P,c_2Eextreal_2EPosInf),c_2Eextreal_2ENegInf))
          & ! [V5v3] :
              ( mem(V5v3,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V5v3)),c_2Eextreal_2ENegInf)) )
          & ! [V6v5] :
              ( mem(V6v5,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,c_2Eextreal_2EPosInf),ap(c_2Eextreal_2ENormal,V6v5))) ) )
       => ! [V7v] :
            ( mem(V7v,ty_2Eextreal_2Eextreal)
           => ! [V8v1] :
                ( mem(V8v1,ty_2Eextreal_2Eextreal)
               => p(ap(ap(V0P,V7v),V8v1)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__le__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ! [V2a] :
              ( mem(V2a,ty_2Eextreal_2Eextreal)
             => ! [V3v2] :
                  ( mem(V3v2,ty_2Erealax_2Ereal)
                 => ! [V4v3] :
                      ( mem(V4v3,ty_2Erealax_2Ereal)
                     => ! [V5v5] :
                          ( mem(V5v5,ty_2Erealax_2Ereal)
                         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2ENormal,V0x)),ap(c_2Eextreal_2ENormal,V1y)))
                            <=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) )
                            & ( p(ap(ap(c_2Eextreal_2Eextreal__le,c_2Eextreal_2ENegInf),V2a))
                            <=> $true )
                            & ( p(ap(ap(c_2Eextreal_2Eextreal__le,c_2Eextreal_2EPosInf),c_2Eextreal_2EPosInf))
                            <=> $true )
                            & ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2ENormal,V3v2)),c_2Eextreal_2EPosInf))
                            <=> $true )
                            & ( p(ap(ap(c_2Eextreal_2Eextreal__le,c_2Eextreal_2EPosInf),c_2Eextreal_2ENegInf))
                            <=> $false )
                            & ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2ENormal,V4v3)),c_2Eextreal_2ENegInf))
                            <=> $false )
                            & ( p(ap(ap(c_2Eextreal_2Eextreal__le,c_2Eextreal_2EPosInf),ap(c_2Eextreal_2ENormal,V5v5)))
                            <=> $false ) ) ) ) ) ) ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__lt__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
          <=> ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V0x)) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__mul__ind,axiom,
    ! [V0P] :
      ( mem(V0P,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool)))
     => ( ( p(ap(ap(V0P,c_2Eextreal_2ENegInf),c_2Eextreal_2ENegInf))
          & p(ap(ap(V0P,c_2Eextreal_2ENegInf),c_2Eextreal_2EPosInf))
          & p(ap(ap(V0P,c_2Eextreal_2EPosInf),c_2Eextreal_2ENegInf))
          & p(ap(ap(V0P,c_2Eextreal_2EPosInf),c_2Eextreal_2EPosInf))
          & ! [V1x] :
              ( mem(V1x,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V1x)),c_2Eextreal_2ENegInf)) )
          & ! [V2y] :
              ( mem(V2y,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,c_2Eextreal_2ENegInf),ap(c_2Eextreal_2ENormal,V2y))) )
          & ! [V3x] :
              ( mem(V3x,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V3x)),c_2Eextreal_2EPosInf)) )
          & ! [V4y] :
              ( mem(V4y,ty_2Erealax_2Ereal)
             => p(ap(ap(V0P,c_2Eextreal_2EPosInf),ap(c_2Eextreal_2ENormal,V4y))) )
          & ! [V5x] :
              ( mem(V5x,ty_2Erealax_2Ereal)
             => ! [V6y] :
                  ( mem(V6y,ty_2Erealax_2Ereal)
                 => p(ap(ap(V0P,ap(c_2Eextreal_2ENormal,V5x)),ap(c_2Eextreal_2ENormal,V6y))) ) ) )
       => ! [V7v] :
            ( mem(V7v,ty_2Eextreal_2Eextreal)
           => ! [V8v1] :
                ( mem(V8v1,ty_2Eextreal_2Eextreal)
               => p(ap(ap(V0P,V7v),V8v1)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__mul__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ( ap(ap(c_2Eextreal_2Eextreal__mul,c_2Eextreal_2ENegInf),c_2Eextreal_2ENegInf) = c_2Eextreal_2EPosInf
            & ap(ap(c_2Eextreal_2Eextreal__mul,c_2Eextreal_2ENegInf),c_2Eextreal_2EPosInf) = c_2Eextreal_2ENegInf
            & ap(ap(c_2Eextreal_2Eextreal__mul,c_2Eextreal_2EPosInf),c_2Eextreal_2ENegInf) = c_2Eextreal_2ENegInf
            & ap(ap(c_2Eextreal_2Eextreal__mul,c_2Eextreal_2EPosInf),c_2Eextreal_2EPosInf) = c_2Eextreal_2EPosInf
            & ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V0x)),c_2Eextreal_2ENegInf) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)),c_2Eextreal_2ENegInf),c_2Eextreal_2EPosInf))
            & ap(ap(c_2Eextreal_2Eextreal__mul,c_2Eextreal_2ENegInf),ap(c_2Eextreal_2ENormal,V1y)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V1y),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)),c_2Eextreal_2ENegInf),c_2Eextreal_2EPosInf))
            & ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V0x)),c_2Eextreal_2EPosInf) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)),c_2Eextreal_2EPosInf),c_2Eextreal_2ENegInf))
            & ap(ap(c_2Eextreal_2Eextreal__mul,c_2Eextreal_2EPosInf),ap(c_2Eextreal_2ENormal,V1y)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V1y),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)),c_2Eextreal_2EPosInf),c_2Eextreal_2ENegInf))
            & ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V0x)),ap(c_2Eextreal_2ENormal,V1y)) = ap(c_2Eextreal_2ENormal,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) ) ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__inv__def,axiom,
    ( ap(c_2Eextreal_2Eextreal__inv,c_2Eextreal_2ENegInf) = ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))
    & ap(c_2Eextreal_2Eextreal__inv,c_2Eextreal_2EPosInf) = ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))
    & ! [V0x] :
        ( mem(V0x,ty_2Erealax_2Ereal)
       => ap(c_2Eextreal_2Eextreal__inv,ap(c_2Eextreal_2ENormal,V0x)) = ap(c_2Eextreal_2ENormal,ap(c_2Erealax_2Einv,V0x)) ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__ainv__def,axiom,
    ( ap(c_2Eextreal_2Eextreal__ainv,c_2Eextreal_2ENegInf) = c_2Eextreal_2EPosInf
    & ap(c_2Eextreal_2Eextreal__ainv,c_2Eextreal_2EPosInf) = c_2Eextreal_2ENegInf
    & ! [V0x] :
        ( mem(V0x,ty_2Erealax_2Ereal)
       => ap(c_2Eextreal_2Eextreal__ainv,ap(c_2Eextreal_2ENormal,V0x)) = ap(c_2Eextreal_2ENormal,ap(c_2Erealax_2Ereal__neg,V0x)) ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__div__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__div,V0x),V1y) = ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(c_2Eextreal_2Eextreal__inv,V1y)) ) ) ).

fof(lameq_f3347,axiom,
    ! [V0R] : ap(f3347,V0R) = ap(c_2Erelation_2EWF(ty_2Eextreal_2Eextreal),V0R) ).

fof(lameq_f3348,axiom,
    ! [V3x] : ap(f3348,V3x) = ap(c_2Ecombin_2EI(ty_2Eextreal_2Eextreal),ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Eabs,V3x))) ).

fof(lameq_f3349,axiom,
    ! [V2a] : ap(f3349,V2a) = ap(ap(ap(ap(c_2Eextreal_2Eextreal__CASE(ty_2Eextreal_2Eextreal),V2a),ap(c_2Ecombin_2EI(ty_2Eextreal_2Eextreal),c_2Eextreal_2EPosInf)),ap(c_2Ecombin_2EI(ty_2Eextreal_2Eextreal),c_2Eextreal_2EPosInf)),f3348) ).

fof(ax_thm_2Eextreal_2Eextreal__abs__primitive__def,axiom,
    c_2Eextreal_2Eextreal__abs = ap(ap(c_2Erelation_2EWFREC(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ap(c_2Emin_2E_40(arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),f3347)),k(arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),f3349)) ).

fof(conj_thm_2Eextreal_2Eextreal__abs__ind,axiom,
    ! [V0P] :
      ( mem(V0P,arr(ty_2Eextreal_2Eextreal,bool))
     => ( ( ! [V1x] :
              ( mem(V1x,ty_2Erealax_2Ereal)
             => p(ap(V0P,ap(c_2Eextreal_2ENormal,V1x))) )
          & p(ap(V0P,c_2Eextreal_2ENegInf))
          & p(ap(V0P,c_2Eextreal_2EPosInf)) )
       => ! [V2v] :
            ( mem(V2v,ty_2Eextreal_2Eextreal)
           => p(ap(V0P,V2v)) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__abs__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ( ap(c_2Eextreal_2Eextreal__abs,ap(c_2Eextreal_2ENormal,V0x)) = ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Eabs,V0x))
        & ap(c_2Eextreal_2Eextreal__abs,c_2Eextreal_2ENegInf) = c_2Eextreal_2EPosInf
        & ap(c_2Eextreal_2Eextreal__abs,c_2Eextreal_2EPosInf) = c_2Eextreal_2EPosInf ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__logr__def,axiom,
    ( ! [V0b] :
        ( mem(V0b,ty_2Erealax_2Ereal)
       => ! [V1x] :
            ( mem(V1x,ty_2Erealax_2Ereal)
           => ap(ap(c_2Eextreal_2Eextreal__logr,V0b),ap(c_2Eextreal_2ENormal,V1x)) = ap(c_2Eextreal_2ENormal,ap(ap(c_2Eutil__prob_2Elogr,V0b),V1x)) ) )
    & ! [V2b] :
        ( mem(V2b,ty_2Erealax_2Ereal)
       => ap(ap(c_2Eextreal_2Eextreal__logr,V2b),c_2Eextreal_2EPosInf) = c_2Eextreal_2EPosInf )
    & ! [V3b] :
        ( mem(V3b,ty_2Erealax_2Ereal)
       => ap(ap(c_2Eextreal_2Eextreal__logr,V3b),c_2Eextreal_2ENegInf) = c_2Eextreal_2ENegInf ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__lg__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(c_2Eextreal_2Eextreal__lg,V0x) = ap(ap(c_2Eextreal_2Eextreal__logr,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0x) ) ).

fof(ax_thm_2Eextreal_2Eextreal__exp__def,axiom,
    ( ! [V0x] :
        ( mem(V0x,ty_2Erealax_2Ereal)
       => ap(c_2Eextreal_2Eextreal__exp,ap(c_2Eextreal_2ENormal,V0x)) = ap(c_2Eextreal_2ENormal,ap(c_2Etransc_2Eexp,V0x)) )
    & ap(c_2Eextreal_2Eextreal__exp,c_2Eextreal_2EPosInf) = c_2Eextreal_2EPosInf
    & ap(c_2Eextreal_2Eextreal__exp,c_2Eextreal_2ENegInf) = ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) ) ).

fof(ax_thm_2Eextreal_2Eextreal__pow__def,axiom,
    ( ! [V0a] :
        ( mem(V0a,ty_2Erealax_2Ereal)
       => ! [V1n] :
            ( mem(V1n,ty_2Enum_2Enum)
           => ap(ap(c_2Eextreal_2Eextreal__pow,ap(c_2Eextreal_2ENormal,V0a)),V1n) = ap(c_2Eextreal_2ENormal,ap(ap(c_2Ereal_2Epow,V0a),V1n)) ) )
    & ! [V2n] :
        ( mem(V2n,ty_2Enum_2Enum)
       => ap(ap(c_2Eextreal_2Eextreal__pow,c_2Eextreal_2EPosInf),V2n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),c_2Eextreal_2EPosInf) )
    & ! [V3n] :
        ( mem(V3n,ty_2Enum_2Enum)
       => ap(ap(c_2Eextreal_2Eextreal__pow,c_2Eextreal_2ENegInf),V3n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3n),c_2Enum_2E0)),ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(c_2Earithmetic_2EEVEN,V3n)),c_2Eextreal_2EPosInf),c_2Eextreal_2ENegInf)) ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__sqrt__def,axiom,
    ( ! [V0x] :
        ( mem(V0x,ty_2Erealax_2Ereal)
       => ap(c_2Eextreal_2Eextreal__sqrt,ap(c_2Eextreal_2ENormal,V0x)) = ap(c_2Eextreal_2ENormal,ap(c_2Etransc_2Esqrt,V0x)) )
    & ap(c_2Eextreal_2Eextreal__sqrt,c_2Eextreal_2EPosInf) = c_2Eextreal_2EPosInf ) ).

fof(conj_thm_2Eextreal_2EREAL__LT__LMUL__0__NEG,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)))
              & p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Erealax_2Ereal__lt,V1y),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ) ) ).

fof(conj_thm_2Eextreal_2EREAL__LT__RMUL__0__NEG,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)))
              & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ) ) ).

fof(conj_thm_2Eextreal_2EREAL__LT__LMUL__NEG__0,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
              & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) )
           => p(ap(ap(c_2Erealax_2Ereal__lt,V1y),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ) ) ).

fof(conj_thm_2Eextreal_2EREAL__LT__RMUL__NEG__0,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
              & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) )
           => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ) ) ).

fof(conj_thm_2Eextreal_2EREAL__LT__LMUL__NEG__0__NEG,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
              & p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) ) ) ).

fof(conj_thm_2Eextreal_2EREAL__LT__RMUL__NEG__0__NEG,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
              & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ) ) ).

fof(conj_thm_2Eextreal_2EREAL__LT__RDIV__EQ__NEG,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ! [V2z] :
              ( mem(V2z,ty_2Erealax_2Ereal)
             => ( p(ap(ap(c_2Erealax_2Ereal__lt,V2z),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
               => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,V1y),V2z)),V0x))
                <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),V1y)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EREAL__LE__RDIV__EQ__NEG,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ! [V2z] :
              ( mem(V2z,ty_2Erealax_2Ereal)
             => ( p(ap(ap(c_2Erealax_2Ereal__lt,V2z),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
               => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,V1y),V2z)),V0x))
                <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),V1y)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EPOW__POS__EVEN,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Erealax_2Ereal)
         => ( p(ap(ap(c_2Erealax_2Ereal__lt,V1x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
           => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2Epow,V1x),V0n)))
            <=> p(ap(c_2Earithmetic_2EEVEN,V0n)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EPOW__NEG__ODD,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Erealax_2Ereal)
         => ( p(ap(ap(c_2Erealax_2Ereal__lt,V1x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
           => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Epow,V1x),V0n)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
            <=> p(ap(c_2Earithmetic_2EODD,V0n)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2ELOGR__MONO__LE,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ! [V2b] :
              ( mem(V2b,ty_2Erealax_2Ereal)
             => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
                  & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y))
                  & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2b)) )
               => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Eutil__prob_2Elogr,V2b),V0x)),ap(ap(c_2Eutil__prob_2Elogr,V2b),V1y)))
                <=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2ELOGR__MONO__LE__IMP,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ! [V2b] :
              ( mem(V2b,ty_2Erealax_2Ereal)
             => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
                  & p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y))
                  & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2b)) )
               => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Eutil__prob_2Elogr,V2b),V0x)),ap(ap(c_2Eutil__prob_2Elogr,V2b),V1y))) ) ) ) ) ).

fof(ax_thm_2Eextreal_2Emono__increasing__def,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ( p(ap(c_2Eextreal_2Emono__increasing,V0f))
      <=> ! [V1m] :
            ( mem(V1m,ty_2Enum_2Enum)
           => ! [V2n] :
                ( mem(V2n,ty_2Enum_2Enum)
               => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n))
                 => p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,V1m)),ap(V0f,V2n))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Emono__increasing__suc,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ( p(ap(c_2Eextreal_2Emono__increasing,V0f))
      <=> ! [V1n] :
            ( mem(V1n,ty_2Enum_2Enum)
           => p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))) ) ) ) ).

fof(ax_thm_2Eextreal_2Emono__decreasing__def,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ( p(ap(c_2Eextreal_2Emono__decreasing,V0f))
      <=> ! [V1m] :
            ( mem(V1m,ty_2Enum_2Enum)
           => ! [V2n] :
                ( mem(V2n,ty_2Enum_2Enum)
               => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n))
                 => p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,V2n)),ap(V0f,V1m))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Emono__decreasing__suc,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ( p(ap(c_2Eextreal_2Emono__decreasing,V0f))
      <=> ! [V1n] :
            ( mem(V1n,ty_2Enum_2Enum)
           => p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,ap(c_2Enum_2ESUC,V1n))),ap(V0f,V1n))) ) ) ) ).

fof(conj_thm_2Eextreal_2Emono__increasing__converges__to__sup,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ! [V1r] :
          ( mem(V1r,ty_2Erealax_2Ereal)
         => ( ( p(ap(c_2Eextreal_2Emono__increasing,V0f))
              & p(ap(ap(c_2Eseq_2E_2D_2D_3E,V0f),V1r)) )
           => V1r = ap(c_2Ereal_2Esup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Erealax_2Ereal),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__cases,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( V0x = c_2Eextreal_2ENegInf
        | V0x = c_2Eextreal_2EPosInf
        | ? [V1r] :
            ( mem(V1r,ty_2Erealax_2Ereal)
            & V0x = ap(c_2Eextreal_2ENormal,V1r) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__eq__zero,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ( ap(c_2Eextreal_2ENormal,V0x) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)
      <=> V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__not__infty,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ( ap(c_2Eextreal_2ENormal,V0x) != c_2Eextreal_2ENegInf
        & ap(c_2Eextreal_2ENormal,V0x) != c_2Eextreal_2EPosInf ) ) ).

fof(conj_thm_2Eextreal_2Enum__not__infty,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ( ap(c_2Eextreal_2Eextreal__of__num,V0n) != c_2Eextreal_2ENegInf
        & ap(c_2Eextreal_2Eextreal__of__num,V0n) != c_2Eextreal_2EPosInf ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__11,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Erealax_2Ereal)
     => ! [V1a_27] :
          ( mem(V1a_27,ty_2Erealax_2Ereal)
         => ( ap(c_2Eextreal_2ENormal,V0a) = ap(c_2Eextreal_2ENormal,V1a_27)
          <=> V0a = V1a_27 ) ) ) ).

fof(conj_thm_2Eextreal_2Emul__rzero,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ).

fof(conj_thm_2Eextreal_2Emul__lzero,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ).

fof(conj_thm_2Eextreal_2Emul__rone,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0x ) ).

fof(conj_thm_2Eextreal_2Emul__lone,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x) = V0x ) ).

fof(conj_thm_2Eextreal_2Eentire,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)
          <=> ( V0x = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)
              | V1y = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__lt__eq,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2ENormal,V0x)),ap(c_2Eextreal_2ENormal,V1y)))
          <=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__refl,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V0x)) ) ).

fof(conj_thm_2Eextreal_2Elt__refl,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ~ p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V0x)) ) ).

fof(conj_thm_2Eextreal_2Ele__infty,axiom,
    ( ! [V0x] :
        ( mem(V0x,ty_2Eextreal_2Eextreal)
       => ( p(ap(ap(c_2Eextreal_2Eextreal__le,c_2Eextreal_2ENegInf),V0x))
          & p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),c_2Eextreal_2EPosInf)) ) )
    & ! [V1x] :
        ( mem(V1x,ty_2Eextreal_2Eextreal)
       => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),c_2Eextreal_2ENegInf))
        <=> V1x = c_2Eextreal_2ENegInf ) )
    & ! [V2x] :
        ( mem(V2x,ty_2Eextreal_2Eextreal)
       => ( p(ap(ap(c_2Eextreal_2Eextreal__le,c_2Eextreal_2EPosInf),V2x))
        <=> V2x = c_2Eextreal_2EPosInf ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__infty,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,c_2Eextreal_2ENegInf),ap(c_2Eextreal_2ENormal,V1y)))
            & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2ENormal,V1y)),c_2Eextreal_2EPosInf))
            & p(ap(ap(c_2Eextreal_2Eextreal__lt,c_2Eextreal_2ENegInf),c_2Eextreal_2EPosInf))
            & ~ p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),c_2Eextreal_2ENegInf))
            & ~ p(ap(ap(c_2Eextreal_2Eextreal__lt,c_2Eextreal_2EPosInf),V0x))
            & ( V0x != c_2Eextreal_2EPosInf
            <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),c_2Eextreal_2EPosInf)) )
            & ( V0x != c_2Eextreal_2ENegInf
            <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,c_2Eextreal_2ENegInf),V0x)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__imp__le,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
           => p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__imp__ne,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
           => V0x != V1y ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__trans,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__trans,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
                  & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),V2z)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elet__trans,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
                  & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),V2z)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__antisym,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
              & p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V0x)) )
          <=> V0x = V1y ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__antisym,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ~ ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),V0x)) ) ) ) ).

fof(conj_thm_2Eextreal_2Elte__trans,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__total,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
            | p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V0x)) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__total,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( V0x = V1y
            | p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
            | p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),V0x)) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__01,axiom,
    p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ).

fof(conj_thm_2Eextreal_2Elt__01,axiom,
    p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ).

fof(conj_thm_2Eextreal_2Ene__01,axiom,
    ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) != ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ).

fof(conj_thm_2Eextreal_2Ele__02,axiom,
    p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ).

fof(conj_thm_2Eextreal_2Elt__02,axiom,
    p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ).

fof(conj_thm_2Eextreal_2Ene__02,axiom,
    ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) != ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ).

fof(conj_thm_2Eextreal_2Ele__num,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(c_2Eextreal_2Eextreal__of__num,V0n))) ) ).

fof(conj_thm_2Eextreal_2Elt__le,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
          <=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
              & V0x != V1y ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__lt,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
          <=> ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
              | V0x = V1y ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__neg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__ainv,V0x)),ap(c_2Eextreal_2Eextreal__ainv,V1y)))
          <=> p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V0x)) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__neg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__ainv,V0x)),ap(c_2Eextreal_2Eextreal__ainv,V1y)))
          <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),V0x)) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__add,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y)) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__add,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y)) )
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Elet__add,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y)) )
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Elte__add,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y)) )
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__add2,axiom,
    ! [V0w] :
      ( mem(V0w,ty_2Eextreal_2Eextreal)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ! [V3z] :
                  ( mem(V3z,ty_2Eextreal_2Eextreal)
                 => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0w),V1x))
                      & p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V3z)) )
                   => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__add,V0w),V2y)),ap(ap(c_2Eextreal_2Eextreal__add,V1x),V3z))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__add2,axiom,
    ! [V0w] :
      ( mem(V0w,ty_2Eextreal_2Eextreal)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ! [V3z] :
                  ( mem(V3z,ty_2Eextreal_2Eextreal)
                 => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0w),V1x))
                      & p(ap(ap(c_2Eextreal_2Eextreal__lt,V2y),V3z)) )
                   => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__add,V0w),V2y)),ap(ap(c_2Eextreal_2Eextreal__add,V1x),V3z))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elet__add2,axiom,
    ! [V0w] :
      ( mem(V0w,ty_2Eextreal_2Eextreal)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ! [V3z] :
                  ( mem(V3z,ty_2Eextreal_2Eextreal)
                 => ( ( V0w != c_2Eextreal_2ENegInf
                      & V0w != c_2Eextreal_2EPosInf
                      & p(ap(ap(c_2Eextreal_2Eextreal__le,V0w),V1x))
                      & p(ap(ap(c_2Eextreal_2Eextreal__lt,V2y),V3z)) )
                   => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__add,V0w),V2y)),ap(ap(c_2Eextreal_2Eextreal__add,V1x),V3z))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elet__add2__alt,axiom,
    ! [V0w] :
      ( mem(V0w,ty_2Eextreal_2Eextreal)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ! [V3z] :
                  ( mem(V3z,ty_2Eextreal_2Eextreal)
                 => ( ( V1x != c_2Eextreal_2ENegInf
                      & V1x != c_2Eextreal_2EPosInf
                      & p(ap(ap(c_2Eextreal_2Eextreal__le,V0w),V1x))
                      & p(ap(ap(c_2Eextreal_2Eextreal__lt,V2y),V3z)) )
                   => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__add,V0w),V2y)),ap(ap(c_2Eextreal_2Eextreal__add,V1x),V3z))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__addr,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( V0x != c_2Eextreal_2ENegInf
              & V0x != c_2Eextreal_2EPosInf )
           => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y)))
            <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__addr__imp,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y))
           => p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__ladd,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y)),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V2z)))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__radd,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V0x)),ap(ap(c_2Eextreal_2Eextreal__add,V2z),V0x)))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__radd__imp,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z))
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V0x)),ap(ap(c_2Eextreal_2Eextreal__add,V2z),V0x))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__ladd__imp,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z))
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y)),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V2z))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__ladd,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y)),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V2z)))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),V2z)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__radd,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V0x)),ap(ap(c_2Eextreal_2Eextreal__add,V2z),V0x)))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),V2z)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__addl,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( V1y != c_2Eextreal_2ENegInf
              & V1y != c_2Eextreal_2EPosInf )
           => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y)))
            <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__lneg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__ainv,V0x)),V1y))
          <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__mul,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y)) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Elet__mul,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y)) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Elte__mul,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y)) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__mul__neg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)))
              & p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Emul__le,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__mul,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y)) )
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__mul__neg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)))
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Emul__lt,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) ) ) ) ).

fof(conj_thm_2Eextreal_2Emul__let,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) ) ) ) ).

fof(conj_thm_2Eextreal_2Emul__lte,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__rmul__imp,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V2z))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V2z)),ap(ap(c_2Eextreal_2Eextreal__mul,V1y),V2z))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__lmul__imp,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V2z))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__mul,V2z),V0x)),ap(ap(c_2Eextreal_2Eextreal__mul,V2z),V1y))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__rmul,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V2z))
                  & V2z != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V2z)),ap(ap(c_2Eextreal_2Eextreal__mul,V1y),V2z)))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__lmul,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
                  & V0x != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V2z)))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),V2z)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__mul2,axiom,
    ! [V0x1] :
      ( mem(V0x1,ty_2Eextreal_2Eextreal)
     => ! [V1x2] :
          ( mem(V1x2,ty_2Eextreal_2Eextreal)
         => ! [V2y1] :
              ( mem(V2y1,ty_2Eextreal_2Eextreal)
             => ! [V3y2] :
                  ( mem(V3y2,ty_2Eextreal_2Eextreal)
                 => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x1))
                      & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V2y1))
                      & V0x1 != c_2Eextreal_2EPosInf
                      & V2y1 != c_2Eextreal_2EPosInf
                      & p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x1),V1x2))
                      & p(ap(ap(c_2Eextreal_2Eextreal__lt,V2y1),V3y2)) )
                   => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__mul,V0x1),V2y1)),ap(ap(c_2Eextreal_2Eextreal__mul,V1x2),V3y2))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eabs__pos,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(c_2Eextreal_2Eextreal__abs,V0x))) ) ).

fof(conj_thm_2Eextreal_2Eabs__refl,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( ap(c_2Eextreal_2Eextreal__abs,V0x) = V0x
      <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x)) ) ) ).

fof(conj_thm_2Eextreal_2Eabs__bounds,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1k] :
          ( mem(V1k,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__abs,V0x)),V1k))
          <=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__ainv,V1k)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1k)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eabs__bounds__lt,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1k] :
          ( mem(V1k,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__abs,V0x)),V1k))
          <=> ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__ainv,V1k)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1k)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__comm,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y) = ap(ap(c_2Eextreal_2Eextreal__add,V1y),V0x) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__assoc,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ap(ap(c_2Eextreal_2Eextreal__add,V0x),ap(ap(c_2Eextreal_2Eextreal__add,V1y),V2z)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y)),V2z) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__not__infty,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( ( V0x != c_2Eextreal_2ENegInf
                & V1y != c_2Eextreal_2ENegInf )
             => ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y) != c_2Eextreal_2ENegInf )
            & ( ( V0x != c_2Eextreal_2EPosInf
                & V1y != c_2Eextreal_2EPosInf )
             => ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y) != c_2Eextreal_2EPosInf ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__rzero,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__add,V0x),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)) = V0x ) ).

fof(conj_thm_2Eextreal_2Eadd__lzero,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__add,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x) = V0x ) ).

fof(conj_thm_2Eextreal_2Eadd__infty,axiom,
    ( ! [V0x] :
        ( mem(V0x,ty_2Eextreal_2Eextreal)
       => ( ap(ap(c_2Eextreal_2Eextreal__add,V0x),c_2Eextreal_2EPosInf) = c_2Eextreal_2EPosInf
          & ap(ap(c_2Eextreal_2Eextreal__add,c_2Eextreal_2EPosInf),V0x) = c_2Eextreal_2EPosInf ) )
    & ! [V1x] :
        ( mem(V1x,ty_2Eextreal_2Eextreal)
       => ( V1x != c_2Eextreal_2EPosInf
         => ( ap(ap(c_2Eextreal_2Eextreal__add,V1x),c_2Eextreal_2ENegInf) = c_2Eextreal_2ENegInf
            & ap(ap(c_2Eextreal_2Eextreal__add,c_2Eextreal_2ENegInf),V1x) = c_2Eextreal_2ENegInf ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__EQ__LADD,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf )
               => ( ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y) = ap(ap(c_2Eextreal_2Eextreal__add,V0x),V2z)
                <=> V1y = V2z ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__rzero,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__sub,V0x),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)) = V0x ) ).

fof(conj_thm_2Eextreal_2Esub__lzero,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__sub,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x) = ap(c_2Eextreal_2Eextreal__ainv,V0x) ) ).

fof(conj_thm_2Eextreal_2Esub__le__imp,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__add,V2z),V0x))) )
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x)),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__le__imp2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V1y != c_2Eextreal_2ENegInf
                  & V1y != c_2Eextreal_2EPosInf
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__add,V2z),V0x))) )
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x)),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__sub__imp,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V0x)),V2z))
               => p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__sub,V2z),V0x))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__sub__imp,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V0x)),V2z))
               => p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),ap(ap(c_2Eextreal_2Eextreal__sub,V2z),V0x))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__lt__imp,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf
                  & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),ap(ap(c_2Eextreal_2Eextreal__add,V2z),V0x))) )
               => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x)),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__lt__imp2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V2z != c_2Eextreal_2ENegInf
                  & V2z != c_2Eextreal_2EPosInf
                  & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),ap(ap(c_2Eextreal_2Eextreal__add,V2z),V0x))) )
               => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x)),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__zero__lt,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x))) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__zero__lt2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( V0x != c_2Eextreal_2ENegInf
              & V0x != c_2Eextreal_2EPosInf
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x))) )
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y)) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__lt__zero,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y))
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__lt__zero2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( V1y != c_2Eextreal_2ENegInf
              & V1y != c_2Eextreal_2EPosInf
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) )
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),V1y)) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__zero__le,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
          <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x))) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__le__zero,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( V1y != c_2Eextreal_2ENegInf
              & V1y != c_2Eextreal_2EPosInf )
           => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
            <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__sub__eq,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__sub,V2z),V0x)))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V0x)),V2z)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__sub__eq2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V2z != c_2Eextreal_2ENegInf
                  & V2z != c_2Eextreal_2EPosInf
                  & V0x != c_2Eextreal_2ENegInf
                  & V1y != c_2Eextreal_2ENegInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__sub,V2z),V0x)))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V0x)),V2z)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__le__eq,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x)),V2z))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__add,V2z),V0x))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__le__eq2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V1y != c_2Eextreal_2ENegInf
                  & V1y != c_2Eextreal_2EPosInf
                  & V0x != c_2Eextreal_2ENegInf
                  & V2z != c_2Eextreal_2ENegInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x)),V2z))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__add,V2z),V0x))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__le__switch,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf
                  & V2z != c_2Eextreal_2ENegInf
                  & V2z != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x)),V2z))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V2z)),V0x)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__le__switch2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf
                  & V1y != c_2Eextreal_2ENegInf
                  & V1y != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x)),V2z))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V2z)),V0x)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__sub,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V2z != c_2Eextreal_2ENegInf
                  & V2z != c_2Eextreal_2EPosInf )
               => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V0x)),V2z))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),ap(ap(c_2Eextreal_2Eextreal__sub,V2z),V0x))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__add2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( V0x != c_2Eextreal_2ENegInf
              & V0x != c_2Eextreal_2EPosInf )
           => ap(ap(c_2Eextreal_2Eextreal__add,V0x),ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x)) = V1y ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__sub,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( V1y != c_2Eextreal_2ENegInf
              & V1y != c_2Eextreal_2EPosInf )
           => ap(ap(c_2Eextreal_2Eextreal__sub,ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y)),V1y) = V0x ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__sub2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( V1y != c_2Eextreal_2ENegInf
              & V1y != c_2Eextreal_2EPosInf )
           => ap(ap(c_2Eextreal_2Eextreal__sub,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V0x)),V1y) = V0x ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__add,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( V1y != c_2Eextreal_2ENegInf
              & V1y != c_2Eextreal_2EPosInf )
           => ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y)),V1y) = V0x ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__sub__add,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y) = ap(ap(c_2Eextreal_2Eextreal__add,V0x),ap(c_2Eextreal_2Eextreal__ainv,V1y)) ) ) ).

fof(conj_thm_2Eextreal_2Esub__0,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)
           => V0x = V1y ) ) ) ).

fof(conj_thm_2Eextreal_2Eneg__neg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(c_2Eextreal_2Eextreal__ainv,ap(c_2Eextreal_2Eextreal__ainv,V0x)) = V0x ) ).

fof(conj_thm_2Eextreal_2Eneg__0,axiom,
    ap(c_2Eextreal_2Eextreal__ainv,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ).

fof(conj_thm_2Eextreal_2Eneg__eq0,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( ap(c_2Eextreal_2Eextreal__ainv,V0x) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)
      <=> V0x = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ) ).

fof(conj_thm_2Eextreal_2Eeq__neg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ap(c_2Eextreal_2Eextreal__ainv,V0x) = ap(c_2Eextreal_2Eextreal__ainv,V1y)
          <=> V0x = V1y ) ) ) ).

fof(conj_thm_2Eextreal_2Eneg__minus1,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(c_2Eextreal_2Eextreal__ainv,V0x) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__ainv,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0x) ) ).

fof(conj_thm_2Eextreal_2Esub__rneg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__sub,V0x),ap(c_2Eextreal_2Eextreal__ainv,V1y)) = ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y) ) ) ).

fof(conj_thm_2Eextreal_2Esub__lneg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( ( V0x != c_2Eextreal_2ENegInf
                & V1y != c_2Eextreal_2ENegInf )
              | ( V0x != c_2Eextreal_2EPosInf
                & V1y != c_2Eextreal_2EPosInf ) )
           => ap(ap(c_2Eextreal_2Eextreal__sub,ap(c_2Eextreal_2Eextreal__ainv,V0x)),V1y) = ap(c_2Eextreal_2Eextreal__ainv,ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y)) ) ) ) ).

fof(conj_thm_2Eextreal_2Eneg__sub,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( ( V0x != c_2Eextreal_2ENegInf
                & V0x != c_2Eextreal_2EPosInf )
              | ( V1y != c_2Eextreal_2ENegInf
                & V1y != c_2Eextreal_2EPosInf ) )
           => ap(c_2Eextreal_2Eextreal__ainv,ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y)) = ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V0x) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__not__infty,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( ( V0x != c_2Eextreal_2ENegInf
                & V1y != c_2Eextreal_2EPosInf )
             => ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y) != c_2Eextreal_2ENegInf )
            & ( ( V0x != c_2Eextreal_2EPosInf
                & V1y != c_2Eextreal_2ENegInf )
             => ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y) != c_2Eextreal_2EPosInf ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__lsub__imp,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z))
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V2z)),ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eeq__sub__ladd__normal,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Erealax_2Ereal)
             => ( V0x = ap(ap(c_2Eextreal_2Eextreal__sub,V1y),ap(c_2Eextreal_2ENormal,V2z))
              <=> ap(ap(c_2Eextreal_2Eextreal__add,V0x),ap(c_2Eextreal_2ENormal,V2z)) = V1y ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eeq__sub__radd,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V1y != c_2Eextreal_2ENegInf
                  & V1y != c_2Eextreal_2EPosInf )
               => ( ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y) = V2z
                <=> V0x = ap(ap(c_2Eextreal_2Eextreal__add,V2z),V1y) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eeq__sub__ladd,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V2z != c_2Eextreal_2ENegInf
                  & V2z != c_2Eextreal_2EPosInf )
               => ( V0x = ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V2z)
                <=> ap(ap(c_2Eextreal_2Eextreal__add,V0x),V2z) = V1y ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eeq__sub__switch,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Erealax_2Ereal)
             => ( V0x = ap(ap(c_2Eextreal_2Eextreal__sub,ap(c_2Eextreal_2ENormal,V2z)),V1y)
              <=> V1y = ap(ap(c_2Eextreal_2Eextreal__sub,ap(c_2Eextreal_2ENormal,V2z)),V0x) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eeq__add__sub__switch,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eextreal_2Eextreal)
     => ! [V1b] :
          ( mem(V1b,ty_2Eextreal_2Eextreal)
         => ! [V2c] :
              ( mem(V2c,ty_2Eextreal_2Eextreal)
             => ! [V3d] :
                  ( mem(V3d,ty_2Eextreal_2Eextreal)
                 => ( ( V1b != c_2Eextreal_2ENegInf
                      & V1b != c_2Eextreal_2EPosInf
                      & V2c != c_2Eextreal_2ENegInf
                      & V2c != c_2Eextreal_2EPosInf )
                   => ( ap(ap(c_2Eextreal_2Eextreal__add,V0a),V1b) = ap(ap(c_2Eextreal_2Eextreal__add,V2c),V3d)
                    <=> ap(ap(c_2Eextreal_2Eextreal__sub,V0a),V2c) = ap(ap(c_2Eextreal_2Eextreal__sub,V3d),V1b) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__refl,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( ( V0x != c_2Eextreal_2ENegInf
          & V0x != c_2Eextreal_2EPosInf )
       => ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V0x) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ) ).

fof(conj_thm_2Eextreal_2Emul__comm,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y) = ap(ap(c_2Eextreal_2Eextreal__mul,V1y),V0x) ) ) ).

fof(conj_thm_2Eextreal_2Emul__assoc,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(ap(c_2Eextreal_2Eextreal__mul,V1y),V2z)) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)),V2z) ) ) ) ).

fof(conj_thm_2Eextreal_2Emul__not__infty,axiom,
    ( ! [V0c] :
        ( mem(V0c,ty_2Erealax_2Ereal)
       => ! [V1y] :
            ( mem(V1y,ty_2Eextreal_2Eextreal)
           => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0c))
                & V1y != c_2Eextreal_2ENegInf )
             => ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V0c)),V1y) != c_2Eextreal_2ENegInf ) ) )
    & ! [V2c] :
        ( mem(V2c,ty_2Erealax_2Ereal)
       => ! [V3y] :
            ( mem(V3y,ty_2Eextreal_2Eextreal)
           => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2c))
                & V3y != c_2Eextreal_2EPosInf )
             => ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V2c)),V3y) != c_2Eextreal_2EPosInf ) ) )
    & ! [V4c] :
        ( mem(V4c,ty_2Erealax_2Ereal)
       => ! [V5y] :
            ( mem(V5y,ty_2Eextreal_2Eextreal)
           => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V4c),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
                & V5y != c_2Eextreal_2ENegInf )
             => ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V4c)),V5y) != c_2Eextreal_2EPosInf ) ) )
    & ! [V6c] :
        ( mem(V6c,ty_2Erealax_2Ereal)
       => ! [V7y] :
            ( mem(V7y,ty_2Eextreal_2Eextreal)
           => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V6c),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
                & V7y != c_2Eextreal_2EPosInf )
             => ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V6c)),V7y) != c_2Eextreal_2ENegInf ) ) ) ) ).

fof(conj_thm_2Eextreal_2Emul__not__infty2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( V0x != c_2Eextreal_2ENegInf
              & V0x != c_2Eextreal_2EPosInf
              & V1y != c_2Eextreal_2ENegInf
              & V1y != c_2Eextreal_2EPosInf )
           => ( ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y) != c_2Eextreal_2ENegInf
              & ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y) != c_2Eextreal_2EPosInf ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__ldistrib__pos,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V2z)) )
               => ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(ap(c_2Eextreal_2Eextreal__add,V1y),V2z)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__ldistrib__neg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V2z),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) )
               => ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(ap(c_2Eextreal_2Eextreal__add,V1y),V2z)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__ldistrib__normal,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( ( V1y != c_2Eextreal_2EPosInf
                    & V2z != c_2Eextreal_2EPosInf )
                  | ( V1y != c_2Eextreal_2ENegInf
                    & V2z != c_2Eextreal_2ENegInf ) )
               => ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V0x)),ap(ap(c_2Eextreal_2Eextreal__add,V1y),V2z)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V0x)),V1y)),ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V0x)),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__ldistrib__normal2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
               => ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V0x)),ap(ap(c_2Eextreal_2Eextreal__add,V1y),V2z)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V0x)),V1y)),ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V0x)),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__rdistrib__normal,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( ( V1y != c_2Eextreal_2EPosInf
                    & V2z != c_2Eextreal_2EPosInf )
                  | ( V1y != c_2Eextreal_2ENegInf
                    & V2z != c_2Eextreal_2ENegInf ) )
               => ap(ap(c_2Eextreal_2Eextreal__mul,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V2z)),ap(c_2Eextreal_2ENormal,V0x)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__mul,V1y),ap(c_2Eextreal_2ENormal,V0x))),ap(ap(c_2Eextreal_2Eextreal__mul,V2z),ap(c_2Eextreal_2ENormal,V0x))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__rdistrib__normal2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
               => ap(ap(c_2Eextreal_2Eextreal__mul,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V2z)),ap(c_2Eextreal_2ENormal,V0x)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__mul,V1y),ap(c_2Eextreal_2ENormal,V0x))),ap(ap(c_2Eextreal_2Eextreal__mul,V2z),ap(c_2Eextreal_2ENormal,V0x))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__ldistrib,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y))
                    & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V2z)) )
                  | ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)))
                    & p(ap(ap(c_2Eextreal_2Eextreal__le,V2z),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) ) )
               => ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(ap(c_2Eextreal_2Eextreal__add,V1y),V2z)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__rdistrib,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1y))
                    & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V2z)) )
                  | ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)))
                    & p(ap(ap(c_2Eextreal_2Eextreal__le,V2z),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) ) )
               => ap(ap(c_2Eextreal_2Eextreal__mul,ap(ap(c_2Eextreal_2Eextreal__add,V1y),V2z)),V0x) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__mul,V1y),V0x)),ap(ap(c_2Eextreal_2Eextreal__mul,V2z),V0x)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Emul__lneg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__ainv,V0x)),V1y) = ap(c_2Eextreal_2Eextreal__ainv,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)) ) ) ).

fof(conj_thm_2Eextreal_2Emul__rneg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(c_2Eextreal_2Eextreal__ainv,V1y)) = ap(c_2Eextreal_2Eextreal__ainv,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)) ) ) ).

fof(conj_thm_2Eextreal_2Eneg__mul2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__ainv,V0x)),ap(c_2Eextreal_2Eextreal__ainv,V1y)) = ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y) ) ) ).

fof(conj_thm_2Eextreal_2Eadd2__sub2,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eextreal_2Eextreal)
     => ! [V1b] :
          ( mem(V1b,ty_2Eextreal_2Eextreal)
         => ! [V2c] :
              ( mem(V2c,ty_2Eextreal_2Eextreal)
             => ! [V3d] :
                  ( mem(V3d,ty_2Eextreal_2Eextreal)
                 => ( ( ( V1b != c_2Eextreal_2EPosInf
                        & V3d != c_2Eextreal_2EPosInf )
                      | ( V1b != c_2Eextreal_2ENegInf
                        & V3d != c_2Eextreal_2ENegInf ) )
                   => ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__sub,V0a),V1b)),ap(ap(c_2Eextreal_2Eextreal__sub,V2c),V3d)) = ap(ap(c_2Eextreal_2Eextreal__sub,ap(ap(c_2Eextreal_2Eextreal__add,V0a),V2c)),ap(ap(c_2Eextreal_2Eextreal__add,V1b),V3d)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__ldistrib,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf
                  & V1y != c_2Eextreal_2ENegInf
                  & V1y != c_2Eextreal_2EPosInf
                  & V2z != c_2Eextreal_2ENegInf
                  & V2z != c_2Eextreal_2EPosInf )
               => ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(ap(c_2Eextreal_2Eextreal__sub,V1y),V2z)) = ap(ap(c_2Eextreal_2Eextreal__sub,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y)),ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esub__rdistrib,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V0x != c_2Eextreal_2EPosInf
                  & V1y != c_2Eextreal_2ENegInf
                  & V1y != c_2Eextreal_2EPosInf
                  & V2z != c_2Eextreal_2ENegInf
                  & V2z != c_2Eextreal_2EPosInf )
               => ap(ap(c_2Eextreal_2Eextreal__mul,ap(ap(c_2Eextreal_2Eextreal__sub,V0x),V1y)),V2z) = ap(ap(c_2Eextreal_2Eextreal__sub,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V2z)),ap(ap(c_2Eextreal_2Eextreal__mul,V1y),V2z)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eextreal__div__eq,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2ENormal,V0x)),ap(c_2Eextreal_2ENormal,V1y)) = ap(c_2Eextreal_2ENormal,ap(ap(c_2Ereal_2E_2F,V0x),V1y)) ) ) ).

fof(conj_thm_2Eextreal_2Einv__one,axiom,
    ap(c_2Eextreal_2Eextreal__inv,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ).

fof(conj_thm_2Eextreal_2Einv__1over,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(c_2Eextreal_2Eextreal__inv,V0x) = ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x) ) ).

fof(conj_thm_2Eextreal_2Ediv__one,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__div,V0x),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0x ) ).

fof(conj_thm_2Eextreal_2Einv__pos,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
          & V0x != c_2Eextreal_2EPosInf )
       => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x))) ) ) ).

fof(conj_thm_2Eextreal_2Erinv__uniq,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y) = ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))
           => V1y = ap(c_2Eextreal_2Eextreal__inv,V0x) ) ) ) ).

fof(conj_thm_2Eextreal_2Elinv__uniq,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y) = ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))
           => V0x = ap(c_2Eextreal_2Eextreal__inv,V1y) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__rdiv,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__mul,V1y),ap(c_2Eextreal_2ENormal,V0x))),V2z))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__div,V2z),ap(c_2Eextreal_2ENormal,V0x)))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__ldiv,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x))
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__mul,V2z),ap(c_2Eextreal_2ENormal,V0x))))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__div,V1y),ap(c_2Eextreal_2ENormal,V0x))),V2z)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__rdiv,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Erealax_2Ereal)
             => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z))
               => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),ap(ap(c_2Eextreal_2Eextreal__div,V1y),ap(c_2Eextreal_2ENormal,V2z))))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(c_2Eextreal_2ENormal,V2z))),V1y)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__ldiv,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Erealax_2Ereal)
             => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z))
               => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__div,V0x),ap(c_2Eextreal_2ENormal,V2z))),V1y))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),ap(ap(c_2Eextreal_2Eextreal__mul,V1y),ap(c_2Eextreal_2ENormal,V2z)))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Elt__rdiv__neg,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Erealax_2Ereal)
             => ( p(ap(ap(c_2Erealax_2Ereal__lt,V2z),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)))
               => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__div,V1y),ap(c_2Eextreal_2ENormal,V2z))),V0x))
                <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(c_2Eextreal_2ENormal,V2z))),V1y)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ediv__add,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( V0x != c_2Eextreal_2ENegInf
                  & V1y != c_2Eextreal_2ENegInf
                  & V2z != ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) )
               => ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__div,V0x),V2z)),ap(ap(c_2Eextreal_2Eextreal__div,V1y),V2z)) = ap(ap(c_2Eextreal_2Eextreal__div,ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y)),V2z) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__inv,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
       => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(c_2Eextreal_2Eextreal__inv,V0x))) ) ) ).

fof(conj_thm_2Eextreal_2Epow__0,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__pow,V0x),c_2Enum_2E0) = ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).

fof(conj_thm_2Eextreal_2Epow__1,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__pow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0x ) ).

fof(conj_thm_2Eextreal_2Epow__2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__pow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V0x) ) ).

fof(conj_thm_2Eextreal_2Epow__zero,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( ap(ap(c_2Eextreal_2Eextreal__pow,V1x),ap(c_2Enum_2ESUC,V0n)) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)
          <=> V1x = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ) ) ).

fof(conj_thm_2Eextreal_2Epow__zero__imp,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( ap(ap(c_2Eextreal_2Eextreal__pow,V1x),V0n) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)
           => V1x = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__pow2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__pow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ).

fof(conj_thm_2Eextreal_2Epow__pos__le,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
       => ! [V1n] :
            ( mem(V1n,ty_2Enum_2Enum)
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__pow,V0x),V1n))) ) ) ) ).

fof(conj_thm_2Eextreal_2Epow__pos__lt,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1n] :
          ( mem(V1n,ty_2Enum_2Enum)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__pow,V0x),V1n))) ) ) ) ).

fof(conj_thm_2Eextreal_2Epow__le,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1x))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V2y)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__pow,V1x),V0n)),ap(ap(c_2Eextreal_2Eextreal__pow,V2y),V0n))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Epow__lt,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1x))
                  & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1x),V2y)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__pow,V1x),ap(c_2Enum_2ESUC,V0n))),ap(ap(c_2Eextreal_2Eextreal__pow,V2y),ap(c_2Enum_2ESUC,V0n)))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Epow__lt2,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ( ( V0n != c_2Enum_2E0
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1x))
                  & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1x),V2y)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__pow,V1x),V0n)),ap(ap(c_2Eextreal_2Eextreal__pow,V2y),V0n))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Epow__le__mono,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1n] :
          ( mem(V1n,ty_2Enum_2Enum)
         => ! [V2m] :
              ( mem(V2m,ty_2Enum_2Enum)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x))
                  & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2m)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__pow,V0x),V1n)),ap(ap(c_2Eextreal_2Eextreal__pow,V0x),V2m))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Epow__pos__even,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V1x),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)))
           => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__pow,V1x),V0n)))
            <=> p(ap(c_2Earithmetic_2EEVEN,V0n)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Epow__neg__odd,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,V1x),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)))
           => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__pow,V1x),V0n)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)))
            <=> p(ap(c_2Earithmetic_2EODD,V0n)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eadd__pow2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__pow,ap(ap(c_2Eextreal_2Eextreal__add,V0x),V1y)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__pow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Eextreal_2Eextreal__pow,V1y),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(ap(c_2Eextreal_2Eextreal__mul,ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0x)),V1y)) ) ) ).

fof(conj_thm_2Eextreal_2Epow__add,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1n] :
          ( mem(V1n,ty_2Enum_2Enum)
         => ! [V2m] :
              ( mem(V2m,ty_2Enum_2Enum)
             => ap(ap(c_2Eextreal_2Eextreal__pow,V0x),ap(ap(c_2Earithmetic_2E_2B,V1n),V2m)) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(ap(c_2Eextreal_2Eextreal__pow,V0x),V1n)),ap(ap(c_2Eextreal_2Eextreal__pow,V0x),V2m)) ) ) ) ).

fof(conj_thm_2Eextreal_2Epow__mul,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ap(ap(c_2Eextreal_2Eextreal__pow,ap(ap(c_2Eextreal_2Eextreal__mul,V1x),V2y)),V0n) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(ap(c_2Eextreal_2Eextreal__pow,V1x),V0n)),ap(ap(c_2Eextreal_2Eextreal__pow,V2y),V0n)) ) ) ) ).

fof(conj_thm_2Eextreal_2Epow__minus1,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ap(ap(c_2Eextreal_2Eextreal__pow,ap(c_2Eextreal_2Eextreal__ainv,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) = ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).

fof(conj_thm_2Eextreal_2Epow__not__infty,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( ( V1x != c_2Eextreal_2ENegInf
              & V1x != c_2Eextreal_2EPosInf )
           => ( ap(ap(c_2Eextreal_2Eextreal__pow,V1x),V0n) != c_2Eextreal_2ENegInf
              & ap(ap(c_2Eextreal_2Eextreal__pow,V1x),V0n) != c_2Eextreal_2EPosInf ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esqrt__pos__le,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
       => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(c_2Eextreal_2Eextreal__sqrt,V0x))) ) ) ).

fof(conj_thm_2Eextreal_2Esqrt__pos__lt,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
       => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(c_2Eextreal_2Eextreal__sqrt,V0x))) ) ) ).

fof(conj_thm_2Eextreal_2Epow2__sqrt,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
       => ap(c_2Eextreal_2Eextreal__sqrt,ap(ap(c_2Eextreal_2Eextreal__pow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = V0x ) ) ).

fof(conj_thm_2Eextreal_2Esqrt__pow2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( ap(ap(c_2Eextreal_2Eextreal__pow,ap(c_2Eextreal_2Eextreal__sqrt,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = V0x
      <=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x)) ) ) ).

fof(conj_thm_2Eextreal_2Esqrt__mono__le,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
              & p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__sqrt,V0x)),ap(c_2Eextreal_2Eextreal__sqrt,V1y))) ) ) ) ).

fof(conj_thm_2Eextreal_2Elogr__not__infty,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1b] :
          ( mem(V1b,ty_2Erealax_2Ereal)
         => ( ( V0x != c_2Eextreal_2ENegInf
              & V0x != c_2Eextreal_2EPosInf )
           => ( ap(ap(c_2Eextreal_2Eextreal__logr,V1b),V0x) != c_2Eextreal_2ENegInf
              & ap(ap(c_2Eextreal_2Eextreal__logr,V1b),V0x) != c_2Eextreal_2EPosInf ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ehalf__between,axiom,
    ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))
    & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
    & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))
    & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).

fof(conj_thm_2Eextreal_2Ethirds__between,axiom,
    ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
    & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
    & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
    & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
    & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
    & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
    & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
    & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).

fof(conj_thm_2Eextreal_2Ehalf__cancel,axiom,
    ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) = ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ).

fof(conj_thm_2Eextreal_2Ethird__cancel,axiom,
    ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) = ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ).

fof(conj_thm_2Eextreal_2Efourth__cancel,axiom,
    ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) = ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ).

fof(conj_thm_2Eextreal_2Equotient__normal,axiom,
    ! [V0n] :
      ( mem(V0n,ty_2Enum_2Enum)
     => ! [V1m] :
          ( mem(V1m,ty_2Enum_2Enum)
         => ap(ap(c_2Eextreal_2Eextreal__div,ap(c_2Eextreal_2Eextreal__of__num,V0n)),ap(c_2Eextreal_2Eextreal__of__num,V1m)) = ap(c_2Eextreal_2ENormal,ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,V0n)),ap(c_2Ereal_2Ereal__of__num,V1m))) ) ) ).

fof(ax_thm_2Eextreal_2Eext__mono__increasing__def,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ( p(ap(c_2Eextreal_2Eext__mono__increasing,V0f))
      <=> ! [V1m] :
            ( mem(V1m,ty_2Enum_2Enum)
           => ! [V2n] :
                ( mem(V2n,ty_2Enum_2Enum)
               => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n))
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V0f,V1m)),ap(V0f,V2n))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eext__mono__increasing__suc,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ( p(ap(c_2Eextreal_2Eext__mono__increasing,V0f))
      <=> ! [V1n] :
            ( mem(V1n,ty_2Enum_2Enum)
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))) ) ) ) ).

fof(ax_thm_2Eextreal_2Eext__mono__decreasing__def,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ( p(ap(c_2Eextreal_2Eext__mono__decreasing,V0f))
      <=> ! [V1m] :
            ( mem(V1m,ty_2Enum_2Enum)
           => ! [V2n] :
                ( mem(V2n,ty_2Enum_2Enum)
               => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n))
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V0f,V2n)),ap(V0f,V1m))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Eext__mono__decreasing__suc,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ( p(ap(c_2Eextreal_2Eext__mono__decreasing,V0f))
      <=> ! [V1n] :
            ( mem(V1n,ty_2Enum_2Enum)
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V0f,ap(c_2Enum_2ESUC,V1n))),ap(V0f,V1n))) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__ARCH,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))
       => ! [V1y] :
            ( mem(V1y,ty_2Eextreal_2Eextreal)
           => ( V1y != c_2Eextreal_2EPosInf
             => ? [V2n] :
                  ( mem(V2n,ty_2Enum_2Enum)
                  & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__of__num,V2n)),V0x))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2ESIMP__REAL__ARCH,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ? [V1n] :
          ( mem(V1n,ty_2Enum_2Enum)
          & p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(c_2Ereal_2Ereal__of__num,V1n))) ) ) ).

fof(conj_thm_2Eextreal_2ESIMP__REAL__ARCH__NEG,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ? [V1n] :
          ( mem(V1n,ty_2Enum_2Enum)
          & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V1n))),V0x)) ) ) ).

fof(conj_thm_2Eextreal_2ESIMP__EXTREAL__ARCH,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( V0x != c_2Eextreal_2EPosInf
       => ? [V1n] :
            ( mem(V1n,ty_2Enum_2Enum)
            & p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),ap(c_2Eextreal_2Eextreal__of__num,V1n))) ) ) ) ).

fof(conj_thm_2Eextreal_2EREAL__ARCH__POW,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ? [V1n] :
          ( mem(V1n,ty_2Enum_2Enum)
          & p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1n))) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__ARCH__POW,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( V0x != c_2Eextreal_2EPosInf
       => ? [V1n] :
            ( mem(V1n,ty_2Enum_2Enum)
            & p(ap(ap(c_2Eextreal_2Eextreal__lt,V0x),ap(ap(c_2Eextreal_2Eextreal__pow,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1n))) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__ARCH__POW__INV,axiom,
    ! [V0e] :
      ( mem(V0e,ty_2Eextreal_2Eextreal)
     => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0e))
       => ? [V1n] :
            ( mem(V1n,ty_2Enum_2Enum)
            & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2ENormal,ap(ap(c_2Ereal_2Epow,ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),V1n))),V0e)) ) ) ) ).

fof(conj_thm_2Eextreal_2EREAL__LE__MUL__EPSILON,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1y] :
          ( mem(V1y,ty_2Erealax_2Ereal)
         => ( ! [V2z] :
                ( mem(V2z,ty_2Erealax_2Ereal)
               => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z))
                    & p(ap(ap(c_2Erealax_2Ereal__lt,V2z),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
                 => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,V2z),V0x)),V1y)) ) )
           => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__epsilon,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ! [V2e] :
                ( mem(V2e,ty_2Eextreal_2Eextreal)
               => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V2e))
                    & V2e != c_2Eextreal_2EPosInf )
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),ap(ap(c_2Eextreal_2Eextreal__add,V1y),V2e))) ) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__mul__epsilon,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ! [V2z] :
                ( mem(V2z,ty_2Eextreal_2Eextreal)
               => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V2z))
                    & p(ap(ap(c_2Eextreal_2Eextreal__lt,V2z),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__mul,V2z),V0x)),V1y)) ) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)) ) ) ) ).

fof(lameq_f3350,axiom,
    ! [A_27a,V0f] :
      ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V2e] :
          ( mem(V2e,A_27a)
         => ! [V3acc] : ap(f3350(A_27a,V0f,V2e),V3acc) = ap(ap(c_2Eextreal_2Eextreal__add,ap(V0f,V2e)),V3acc) ) ) ).

fof(lameq_f3351,axiom,
    ! [A_27a,V0f] :
      ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V2e] : ap(f3351(A_27a,V0f),V2e) = f3350(A_27a,V0f,V2e) ) ).

fof(ax_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__DEF,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1s] :
              ( mem(V1s,arr(A_27a,bool))
             => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V1s) = ap(ap(ap(c_2Epred__set_2EITSET(A_27a,ty_2Eextreal_2Eextreal),f3351(A_27a,V0f)),V1s),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__THM,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ( ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),c_2Epred__set_2EEMPTY(A_27a)) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)
            & ! [V1e] :
                ( mem(V1e,A_27a)
               => ! [V2s] :
                    ( mem(V2s,arr(A_27a,bool))
                   => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V2s))
                     => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1e),V2s)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(V0f,V1e)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1e))) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__NOT__NEG__INF,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1s] :
              ( mem(V1s,arr(A_27a,bool))
             => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
                  & ! [V2x] :
                      ( mem(V2x,A_27a)
                     => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
                       => ap(V0f,V2x) != c_2Eextreal_2ENegInf ) ) )
               => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V1s) != c_2Eextreal_2ENegInf ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__NOT__POS__INF,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1s] :
              ( mem(V1s,arr(A_27a,bool))
             => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
                  & ! [V2x] :
                      ( mem(V2x,A_27a)
                     => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
                       => ap(V0f,V2x) != c_2Eextreal_2EPosInf ) ) )
               => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V1s) != c_2Eextreal_2EPosInf ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__NOT__INFTY,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1s] :
              ( mem(V1s,arr(A_27a,bool))
             => ( ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
                    & ! [V2x] :
                        ( mem(V2x,A_27a)
                       => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
                         => ap(V0f,V2x) != c_2Eextreal_2ENegInf ) ) )
                 => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V1s) != c_2Eextreal_2ENegInf )
                & ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
                    & ! [V3x] :
                        ( mem(V3x,A_27a)
                       => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s))
                         => ap(V0f,V3x) != c_2Eextreal_2EPosInf ) ) )
                 => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V1s) != c_2Eextreal_2EPosInf ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__SING,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1e] :
              ( mem(V1e,A_27a)
             => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1e),c_2Epred__set_2EEMPTY(A_27a))) = ap(V0f,V1e) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__POS,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1s] :
              ( mem(V1s,arr(A_27a,bool))
             => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
                  & ! [V2x] :
                      ( mem(V2x,A_27a)
                     => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
                       => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V0f,V2x))) ) ) )
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V1s))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__SPOS,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1s] :
              ( mem(V1s,arr(A_27a,bool))
             => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
                  & V1s != c_2Epred__set_2EEMPTY(A_27a)
                  & ! [V2x] :
                      ( mem(V2x,A_27a)
                     => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
                       => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V0f,V2x))) ) ) )
               => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V1s))) ) ) ) ) ).

fof(lameq_f3352,axiom,
    ! [A_27a,V2f] :
      ( mem(V2f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V1P] :
          ( mem(V1P,arr(A_27a,bool))
         => ! [V4x] : ap(f3352(A_27a,V2f,V1P),V4x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(V1P,V4x)),ap(V2f,V4x)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__IF__ELIM,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ! [V1P] :
              ( mem(V1P,arr(A_27a,bool))
             => ! [V2f] :
                  ( mem(V2f,arr(A_27a,ty_2Eextreal_2Eextreal))
                 => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
                      & ! [V3x] :
                          ( mem(V3x,A_27a)
                         => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s))
                           => p(ap(V1P,V3x)) ) ) )
                   => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3352(A_27a,V2f,V1P)),V0s) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V2f),V0s) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__FINITE__SAME,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ! [V2p] :
                    ( mem(V2p,A_27a)
                   => ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2p),V0s))
                        & ! [V3q] :
                            ( mem(V3q,A_27a)
                           => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3q),V0s))
                             => ap(V1f,V2p) = ap(V1f,V3q) ) ) )
                     => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Epred__set_2ECARD(A_27a),V0s))),ap(V1f,V2p)) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__FINITE__CONST,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0P] :
          ( mem(V0P,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0P))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ! [V2x] :
                    ( mem(V2x,ty_2Eextreal_2Eextreal)
                   => ( ! [V3y] :
                          ( mem(V3y,A_27a)
                         => ap(V1f,V3y) = V2x )
                     => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0P) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Epred__set_2ECARD(A_27a),V0P))),V2x) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__ZERO,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),k(A_27a,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))),V0s) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__0,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1s] :
              ( mem(V1s,arr(A_27a,bool))
             => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
                  & ! [V2x] :
                      ( mem(V2x,A_27a)
                     => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
                       => ap(V0f,V2x) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ) )
               => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V1s) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ) ) ) ).

fof(lameq_f3353,axiom,
    ! [A_27a,V1f] :
      ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ! [V2x] : ap(f3353(A_27a,V1f,V0s),V2x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)),ap(V1f,V2x)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__IN__IF,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3353(A_27a,V1f,V0s)),V0s) ) ) ) ) ).

fof(lameq_f3354,axiom,
    ! [A_27a,V1f] :
      ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V2c] :
          ( mem(V2c,ty_2Erealax_2Ereal)
         => ! [V4x] : ap(f3354(A_27a,V1f,V2c),V4x) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V2c)),ap(V1f,V4x)) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__CMUL,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ! [V2c] :
                    ( mem(V2c,ty_2Erealax_2Ereal)
                   => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2c))
                        | ! [V3x] :
                            ( mem(V3x,A_27a)
                           => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s))
                             => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V1f,V3x))) ) ) )
                     => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3354(A_27a,V1f,V2c)),V0s) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V2c)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s)) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__CMUL2,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ! [V1f] :
              ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
             => ! [V2c] :
                  ( mem(V2c,ty_2Erealax_2Ereal)
                 => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
                      & ! [V3x] :
                          ( mem(V3x,A_27a)
                         => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s))
                           => ap(V1f,V3x) != c_2Eextreal_2ENegInf ) ) )
                   => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3354(A_27a,V1f,V2c)),V0s) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V2c)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__IMAGE,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [A_27b] :
          ( ne(A_27b)
         => ! [V0s] :
              ( mem(V0s,arr(A_27a,bool))
             => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
               => ! [V1f_27] :
                    ( mem(V1f_27,arr(A_27a,A_27b))
                   => ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V1f_27),V0s),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1f_27),V0s)))
                     => ! [V2f] :
                          ( mem(V2f,arr(A_27b,ty_2Eextreal_2Eextreal))
                         => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27b),V2f),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1f_27),V0s)) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Eextreal_2Eextreal,A_27b),V2f),V1f_27)),V0s) ) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__DISJOINT__UNION,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ! [V1s_27] :
              ( mem(V1s_27,arr(A_27a,bool))
             => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
                  & p(ap(c_2Epred__set_2EFINITE(A_27a),V1s_27))
                  & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1s_27)) )
               => ! [V2f] :
                    ( mem(V2f,arr(A_27a,ty_2Eextreal_2Eextreal))
                   => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V2f),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1s_27)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V2f),V0s)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V2f),V1s_27)) ) ) ) ) ) ).

fof(lameq_f3355,axiom,
    ! [A_27a,V0s] :
      ( mem(V0s,arr(A_27a,bool))
     => ! [V1x] : ap(f3355(A_27a,V0s),V1x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)),ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__EQ__CARD,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3355(A_27a,V0s)),V0s) = ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Epred__set_2ECARD(A_27a),V0s)) ) ) ) ).

fof(lameq_f3356,axiom,
    ! [A_27a,V0s] :
      ( mem(V0s,arr(A_27a,bool))
     => ! [V1x] : ap(f3356(A_27a,V0s),V1x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)),ap(c_2Eextreal_2Eextreal__inv,ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Epred__set_2ECARD(A_27a),V0s)))),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__INV__CARD__EQ__1,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( ( V0s != c_2Epred__set_2EEMPTY(A_27a)
              & p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) )
           => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3356(A_27a,V0s)),V0s) = ap(c_2Eextreal_2Eextreal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) ).

fof(lameq_f3357,axiom,
    ! [A_27a,V1f] :
      ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V2p] : ap(f3357(A_27a,V1f),V2p) = ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),ap(V1f,V2p)),ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__INTER__NONZERO,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),f3357(A_27a,V1f))) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__INTER__ELIM,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ! [V2s_27] :
                    ( mem(V2s_27,arr(A_27a,bool))
                   => ( ! [V3x] :
                          ( mem(V3x,A_27a)
                         => ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V2s_27))
                           => ap(V1f,V3x) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) )
                     => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2s_27)) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__ZERO__DIFF,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ! [V2t] :
                    ( mem(V2t,arr(A_27a,bool))
                   => ( ! [V3x] :
                          ( mem(V3x,A_27a)
                         => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V2t))
                           => ap(V1f,V3x) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) )
                     => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V2t)) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__MONO,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ! [V2f_27] :
                    ( mem(V2f_27,arr(A_27a,ty_2Eextreal_2Eextreal))
                   => ( ! [V3x] :
                          ( mem(V3x,A_27a)
                         => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s))
                           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V1f,V3x)),ap(V2f_27,V3x))) ) )
                     => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V2f_27),V0s))) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__MONO__SET,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1s] :
              ( mem(V1s,arr(A_27a,bool))
             => ! [V2t] :
                  ( mem(V2t,arr(A_27a,bool))
                 => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
                      & p(ap(c_2Epred__set_2EFINITE(A_27a),V2t))
                      & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t))
                      & ! [V3x] :
                          ( mem(V3x,A_27a)
                         => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V2t))
                           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V0f,V3x))) ) ) )
                   => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V1s)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V2t))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__EQ,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ! [V2f_27] :
                    ( mem(V2f_27,arr(A_27a,ty_2Eextreal_2Eextreal))
                   => ( ! [V3x] :
                          ( mem(V3x,A_27a)
                         => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s))
                           => ap(V1f,V3x) = ap(V2f_27,V3x) ) )
                     => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V2f_27),V0s) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__POS__MEM__LE,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1s] :
              ( mem(V1s,arr(A_27a,bool))
             => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
                  & ! [V2x] :
                      ( mem(V2x,A_27a)
                     => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))
                       => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V0f,V2x))) ) ) )
               => ! [V3x] :
                    ( mem(V3x,A_27a)
                   => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s))
                     => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V0f,V3x)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V0f),V1s))) ) ) ) ) ) ) ).

fof(lameq_f3358,axiom,
    ! [A_27a,V1f] :
      ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V2f_27] :
          ( mem(V2f_27,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V3x] : ap(f3358(A_27a,V1f,V2f_27),V3x) = ap(ap(c_2Eextreal_2Eextreal__add,ap(V1f,V3x)),ap(V2f_27,V3x)) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__ADD,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ! [V2f_27] :
                    ( mem(V2f_27,arr(A_27a,ty_2Eextreal_2Eextreal))
                   => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3358(A_27a,V1f,V2f_27)),V0s) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V2f_27),V0s)) ) ) ) ) ) ).

fof(lameq_f3359,axiom,
    ! [A_27a,V1f] :
      ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V2f_27] :
          ( mem(V2f_27,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V5x] : ap(f3359(A_27a,V1f,V2f_27),V5x) = ap(ap(c_2Eextreal_2Eextreal__sub,ap(V1f,V5x)),ap(V2f_27,V5x)) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__SUB,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
           => ! [V1f] :
                ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
               => ! [V2f_27] :
                    ( mem(V2f_27,arr(A_27a,ty_2Eextreal_2Eextreal))
                   => ( ( ! [V3x] :
                            ( mem(V3x,A_27a)
                           => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s))
                             => ap(V2f_27,V3x) != c_2Eextreal_2ENegInf ) )
                        | ! [V4x] :
                            ( mem(V4x,A_27a)
                           => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V0s))
                             => ap(V2f_27,V4x) != c_2Eextreal_2EPosInf ) ) )
                     => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3359(A_27a,V1f,V2f_27)),V0s) = ap(ap(c_2Eextreal_2Eextreal__sub,ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s)),ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V2f_27),V0s)) ) ) ) ) ) ) ).

fof(lameq_f3360,axiom,
    ! [A_27b,A_27a,V2f] :
      ( mem(V2f,arr(A_27a,arr(A_27b,ty_2Eextreal_2Eextreal)))
     => ! [V1s_27] :
          ( mem(V1s_27,arr(A_27b,bool))
         => ! [V3x] : ap(f3360(A_27b,A_27a,V2f,V1s_27),V3x) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27b),ap(V2f,V3x)),V1s_27) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__EXTREAL__SUM__IMAGE,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [A_27b] :
          ( ne(A_27b)
         => ! [V0s] :
              ( mem(V0s,arr(A_27a,bool))
             => ! [V1s_27] :
                  ( mem(V1s_27,arr(A_27b,bool))
                 => ! [V2f] :
                      ( mem(V2f,arr(A_27a,arr(A_27b,ty_2Eextreal_2Eextreal)))
                     => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
                          & p(ap(c_2Epred__set_2EFINITE(A_27b),V1s_27)) )
                       => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3360(A_27b,A_27a,V2f,V1s_27)),V0s) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Epair_2Eprod(A_27a,A_27b)),f3092(A_27a,A_27b,V2f)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0s),V1s_27)) ) ) ) ) ) ) ).

fof(lameq_f3361,axiom,
    ! [A_27a,V0f] :
      ( mem(V0f,arr(A_27a,ty_2Erealax_2Ereal))
     => ! [V2x] : ap(f3361(A_27a,V0f),V2x) = ap(c_2Eextreal_2ENormal,ap(V0f,V2x)) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__NORMAL,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Erealax_2Ereal))
         => ! [V1s] :
              ( mem(V1s,arr(A_27a,bool))
             => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
               => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3361(A_27a,V0f)),V1s) = ap(c_2Eextreal_2ENormal,ap(ap(c_2Ereal__sigma_2EREAL__SUM__IMAGE(A_27a),V0f),V1s)) ) ) ) ) ).

fof(lameq_f3362,axiom,
    ! [A_27a,V1f] :
      ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ! [V3x] : ap(f3362(A_27a,V1f,V0s,V2z),V3x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s)),ap(V1f,V3x)),V2z) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__IN__IF__ALT,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ! [V1f] :
              ( mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal))
             => ! [V2z] :
                  ( mem(V2z,ty_2Eextreal_2Eextreal)
                 => ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
                   => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),V1f),V0s) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(A_27a),f3362(A_27a,V1f,V0s,V2z)),V0s) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__CROSS__SYM,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [A_27b] :
          ( ne(A_27b)
         => ! [V0f] :
              ( mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Eextreal_2Eextreal))
             => ! [V1s1] :
                  ( mem(V1s1,arr(A_27a,bool))
                 => ! [V2s2] :
                      ( mem(V2s2,arr(A_27b,bool))
                     => ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s1))
                          & p(ap(c_2Epred__set_2EFINITE(A_27b),V2s2)) )
                       => ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Eextreal_2Eextreal),f3103(A_27b,A_27a,V0f))),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V1s1),V2s2)) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Epair_2Eprod(A_27b,A_27a)),ap(c_2Epair_2EUNCURRY(A_27b,A_27a,ty_2Eextreal_2Eextreal),f3105(A_27a,A_27b,V0f))),ap(ap(c_2Epred__set_2ECROSS(A_27b,A_27a),V2s2),V1s1)) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2EEXTREAL__SUM__IMAGE__COUNT,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ( ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Enum_2Enum),V0f),ap(c_2Epred__set_2Ecount,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(ap(c_2Eextreal_2Eextreal__add,ap(V0f,c_2Enum_2E0)),ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))
        & ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Enum_2Enum),V0f),ap(c_2Epred__set_2Ecount,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__add,ap(V0f,c_2Enum_2E0)),ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))
        & ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Enum_2Enum),V0f),ap(c_2Epred__set_2Ecount,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__add,ap(V0f,c_2Enum_2E0)),ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
        & ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Enum_2Enum),V0f),ap(c_2Epred__set_2Ecount,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) = ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__add,ap(ap(c_2Eextreal_2Eextreal__add,ap(V0f,c_2Enum_2E0)),ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ).

fof(lameq_f3363,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] : ap(f3363(V0p,V1x),V2y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V0p,V2y)),ap(ap(c_2Eextreal_2Eextreal__le,V2y),V1x)) ) ) ).

fof(lameq_f3364,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1x] : ap(f3364(V0p),V1x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eextreal_2Eextreal),f3363(V0p,V1x))),ap(ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),V1x),c_2Eextreal_2EPosInf)) ) ).

fof(lameq_f3365,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V3x] : ap(f3365(V0p),V3x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V0p,V3x)),ap(ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),V3x),c_2Eextreal_2ENegInf)) ) ).

fof(lameq_f3366,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V4r] : ap(f3366(V0p),V4r) = ap(V0p,ap(c_2Eextreal_2ENormal,V4r)) ) ).

fof(ax_thm_2Eextreal_2Eextreal__sup__def,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ap(c_2Eextreal_2Eextreal__sup,V0p) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(c_2Ebool_2E_21(ty_2Eextreal_2Eextreal),f3364(V0p))),c_2Eextreal_2EPosInf),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(c_2Ebool_2E_21(ty_2Eextreal_2Eextreal),f3365(V0p))),c_2Eextreal_2ENegInf),ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Esup,f3366(V0p))))) ) ).

fof(ax_thm_2Eextreal_2Eextreal__inf__def,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ap(c_2Eextreal_2Eextreal__inf,V0p) = ap(c_2Eextreal_2Eextreal__ainv,ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),c_2Eextreal_2Eextreal__ainv),V0p))) ) ).

fof(conj_thm_2Eextreal_2Ele__sup__imp,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( p(ap(V0p,V1x))
           => p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),ap(c_2Eextreal_2Eextreal__sup,V0p))) ) ) ) ).

fof(conj_thm_2Eextreal_2Esup__le,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__sup,V0p)),V1x))
          <=> ! [V2y] :
                ( mem(V2y,ty_2Eextreal_2Eextreal)
               => ( p(ap(V0p,V2y))
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V1x)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__sup,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),ap(c_2Eextreal_2Eextreal__sup,V0p)))
          <=> ! [V2y] :
                ( mem(V2y,ty_2Eextreal_2Eextreal)
               => ( ! [V3z] :
                      ( mem(V3z,ty_2Eextreal_2Eextreal)
                     => ( p(ap(V0p,V3z))
                       => p(ap(ap(c_2Eextreal_2Eextreal__le,V3z),V2y)) ) )
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V2y)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esup__eq,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( ap(c_2Eextreal_2Eextreal__sup,V0p) = V1x
          <=> ( ! [V2y] :
                  ( mem(V2y,ty_2Eextreal_2Eextreal)
                 => ( p(ap(V0p,V2y))
                   => p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V1x)) ) )
              & ! [V3y] :
                  ( mem(V3y,ty_2Eextreal_2Eextreal)
                 => ( ! [V4z] :
                        ( mem(V4z,ty_2Eextreal_2Eextreal)
                       => ( p(ap(V0p,V4z))
                         => p(ap(ap(c_2Eextreal_2Eextreal__le,V4z),V3y)) ) )
                   => p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V3y)) ) ) ) ) ) ) ).

fof(lameq_f3367,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] : ap(f3367(V0x),V1y) = ap(ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),V1y),V0x) ) ).

fof(conj_thm_2Eextreal_2Esup__const,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(c_2Eextreal_2Eextreal__sup,f3367(V0x)) = V0x ) ).

fof(conj_thm_2Eextreal_2Esup__const__alt,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1z] :
          ( mem(V1z,ty_2Eextreal_2Eextreal)
         => ( ( ? [V2x] :
                  ( mem(V2x,ty_2Eextreal_2Eextreal)
                  & p(ap(V0p,V2x)) )
              & ! [V3x] :
                  ( mem(V3x,ty_2Eextreal_2Eextreal)
                 => ( p(ap(V0p,V3x))
                   => V3x = V1z ) ) )
           => ap(c_2Eextreal_2Eextreal__sup,V0p) = V1z ) ) ) ).

fof(conj_thm_2Eextreal_2Esup__const__over__set,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ! [V1k] :
              ( mem(V1k,ty_2Eextreal_2Eextreal)
             => ( V0s != c_2Epred__set_2EEMPTY(A_27a)
               => ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Eextreal_2Eextreal),k(A_27a,V1k)),V0s)) = V1k ) ) ) ) ).

fof(lameq_f3368,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1n] : ap(f3368(V0x),V1n) = ap(ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),V0x),ap(c_2Eextreal_2Eextreal__of__num,V1n)) ) ).

fof(lameq_f3369,axiom,
    ! [V0x] : ap(f3369,V0x) = ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f3368(V0x)) ).

fof(conj_thm_2Eextreal_2Esup__num,axiom,
    ap(c_2Eextreal_2Eextreal__sup,f3369) = c_2Eextreal_2EPosInf ).

fof(conj_thm_2Eextreal_2Esup__le__sup__imp,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1q] :
          ( mem(V1q,arr(ty_2Eextreal_2Eextreal,bool))
         => ( ! [V2x] :
                ( mem(V2x,ty_2Eextreal_2Eextreal)
               => ( p(ap(V0p,V2x))
                 => ? [V3y] :
                      ( mem(V3y,ty_2Eextreal_2Eextreal)
                      & p(ap(V1q,V3y))
                      & p(ap(ap(c_2Eextreal_2Eextreal__le,V2x),V3y)) ) ) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__sup,V0p)),ap(c_2Eextreal_2Eextreal__sup,V1q))) ) ) ) ).

fof(conj_thm_2Eextreal_2Esup__mono,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1q] :
          ( mem(V1q,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
         => ( ! [V2n] :
                ( mem(V2n,ty_2Enum_2Enum)
               => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V0p,V2n)),ap(V1q,V2n))) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),V0p),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))),ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),V1q),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))) ) ) ) ).

fof(lameq_f3370,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V3n] : ap(f3370(V0f),V3n) = ap(V0f,ap(c_2Enum_2ESUC,V3n)) ) ).

fof(conj_thm_2Eextreal_2Esup__suc,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ( ! [V1m] :
            ( mem(V1m,ty_2Enum_2Enum)
           => ! [V2n] :
                ( mem(V2n,ty_2Enum_2Enum)
               => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n))
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V0f,V1m)),ap(V0f,V2n))) ) ) )
       => ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),f3370(V0f)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) = ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) ) ) ).

fof(lameq_f3371,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ! [V2n] : ap(f3371(V0f),V2n) = ap(c_2Eextreal_2ENormal,ap(V0f,V2n)) ) ).

fof(conj_thm_2Eextreal_2Esup__seq,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ! [V1l] :
          ( mem(V1l,ty_2Erealax_2Ereal)
         => ( p(ap(c_2Eextreal_2Emono__increasing,V0f))
           => ( p(ap(ap(c_2Eseq_2E_2D_2D_3E,V0f),V1l))
            <=> ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),f3371(V0f)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) = ap(c_2Eextreal_2ENormal,V1l) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esup__lt__infty,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__sup,V0p)),c_2Eextreal_2EPosInf))
       => ! [V1x] :
            ( mem(V1x,ty_2Eextreal_2Eextreal)
           => ( p(ap(V0p,V1x))
             => p(ap(ap(c_2Eextreal_2Eextreal__lt,V1x),c_2Eextreal_2EPosInf)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esup__max,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1z] :
          ( mem(V1z,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(V0p,V1z))
              & ! [V2x] :
                  ( mem(V2x,ty_2Eextreal_2Eextreal)
                 => ( p(ap(V0p,V2x))
                   => p(ap(ap(c_2Eextreal_2Eextreal__le,V2x),V1z)) ) ) )
           => ap(c_2Eextreal_2Eextreal__sup,V0p) = V1z ) ) ) ).

fof(lameq_f3372,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1g] :
          ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
         => ! [V6n] : ap(f3372(V0f,V1g),V6n) = ap(ap(c_2Eextreal_2Eextreal__add,ap(V0f,V6n)),ap(V1g,V6n)) ) ) ).

fof(conj_thm_2Eextreal_2Esup__add__mono,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1g] :
          ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
         => ( ( ! [V2n] :
                  ( mem(V2n,ty_2Enum_2Enum)
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V0f,V2n))) )
              & ! [V3n] :
                  ( mem(V3n,ty_2Enum_2Enum)
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V0f,V3n)),ap(V0f,ap(c_2Enum_2ESUC,V3n)))) )
              & ! [V4n] :
                  ( mem(V4n,ty_2Enum_2Enum)
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V1g,V4n))) )
              & ! [V5n] :
                  ( mem(V5n,ty_2Enum_2Enum)
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V1g,V5n)),ap(V1g,ap(c_2Enum_2ESUC,V5n)))) ) )
           => ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),f3372(V0f,V1g)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) = ap(ap(c_2Eextreal_2Eextreal__add,ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))),ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),V1g),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) ) ) ) ).

fof(lameq_f3373,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal)))
     => ! [V6n] :
          ( mem(V6n,ty_2Enum_2Enum)
         => ! [V7i] : ap(f3373(V0f,V6n),V7i) = ap(ap(V0f,V7i),V6n) ) ) ).

fof(lameq_f3374,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal)))
     => ! [V1s] :
          ( mem(V1s,arr(ty_2Enum_2Enum,bool))
         => ! [V6n] : ap(f3374(V0f,V1s),V6n) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Enum_2Enum),f3373(V0f,V6n)),V1s) ) ) ).

fof(lameq_f3375,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal)))
     => ! [V8i] : ap(f3375(V0f),V8i) = ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),ap(V0f,V8i)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) ) ).

fof(conj_thm_2Eextreal_2Esup__sum__mono,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal)))
     => ! [V1s] :
          ( mem(V1s,arr(ty_2Enum_2Enum,bool))
         => ( ( p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V1s))
              & ! [V2i] :
                  ( mem(V2i,ty_2Enum_2Enum)
                 => ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V2i),V1s))
                   => ! [V3n] :
                        ( mem(V3n,ty_2Enum_2Enum)
                       => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(ap(V0f,V2i),V3n))) ) ) )
              & ! [V4i] :
                  ( mem(V4i,ty_2Enum_2Enum)
                 => ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V4i),V1s))
                   => ! [V5n] :
                        ( mem(V5n,ty_2Enum_2Enum)
                       => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(V0f,V4i),V5n)),ap(ap(V0f,V4i),ap(c_2Enum_2ESUC,V5n)))) ) ) ) )
           => ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),f3374(V0f,V1s)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Enum_2Enum),f3375(V0f)),V1s) ) ) ) ).

fof(conj_thm_2Eextreal_2Esup__le__mono,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1z] :
          ( mem(V1z,ty_2Eextreal_2Eextreal)
         => ( ( ! [V2n] :
                  ( mem(V2n,ty_2Enum_2Enum)
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V0f,V2n)),ap(V0f,ap(c_2Enum_2ESUC,V2n)))) )
              & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1z),ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))) )
           => ? [V3n] :
                ( mem(V3n,ty_2Enum_2Enum)
                & p(ap(ap(c_2Eextreal_2Eextreal__le,V1z),ap(V0f,V3n))) ) ) ) ) ).

fof(lameq_f3376,axiom,
    ! [A_27a,V0f] :
      ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V1c] :
          ( mem(V1c,ty_2Erealax_2Ereal)
         => ! [V2n] : ap(f3376(A_27a,V0f,V1c),V2n) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V1c)),ap(V0f,V2n)) ) ) ).

fof(conj_thm_2Eextreal_2Esup__cmul,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1c] :
              ( mem(V1c,ty_2Erealax_2Ereal)
             => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1c))
               => ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Eextreal_2Eextreal),f3376(A_27a,V0f,V1c)),c_2Epred__set_2EUNIV(A_27a))) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V1c)),ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Eextreal_2Eextreal),V0f),c_2Epred__set_2EUNIV(A_27a)))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Esup__lt,axiom,
    ! [V0P] :
      ( mem(V0P,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ? [V2x] :
                ( mem(V2x,ty_2Eextreal_2Eextreal)
                & p(ap(V0P,V2x))
                & p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),V2x)) )
          <=> p(ap(ap(c_2Eextreal_2Eextreal__lt,V1y),ap(c_2Eextreal_2Eextreal__sup,V0P))) ) ) ) ).

fof(conj_thm_2Eextreal_2Esup__lt__epsilon,axiom,
    ! [V0P] :
      ( mem(V0P,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1e] :
          ( mem(V1e,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1e))
              & ? [V2x] :
                  ( mem(V2x,ty_2Eextreal_2Eextreal)
                  & p(ap(V0P,V2x))
                  & V2x != c_2Eextreal_2ENegInf )
              & ap(c_2Eextreal_2Eextreal__sup,V0P) != c_2Eextreal_2EPosInf )
           => ? [V3x] :
                ( mem(V3x,ty_2Eextreal_2Eextreal)
                & p(ap(V0P,V3x))
                & p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(c_2Eextreal_2Eextreal__sup,V0P)),ap(ap(c_2Eextreal_2Eextreal__add,V3x),V1e))) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Einf__le__imp,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( p(ap(V0p,V1x))
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__inf,V0p)),V1x)) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__inf,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),ap(c_2Eextreal_2Eextreal__inf,V0p)))
          <=> ! [V2y] :
                ( mem(V2y,ty_2Eextreal_2Eextreal)
               => ( p(ap(V0p,V2y))
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V2y)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Einf__le,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__inf,V0p)),V1x))
          <=> ! [V2y] :
                ( mem(V2y,ty_2Eextreal_2Eextreal)
               => ( ! [V3z] :
                      ( mem(V3z,ty_2Eextreal_2Eextreal)
                     => ( p(ap(V0p,V3z))
                       => p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V3z)) ) )
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V1x)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Einf__eq,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ( ap(c_2Eextreal_2Eextreal__inf,V0p) = V1x
          <=> ( ! [V2y] :
                  ( mem(V2y,ty_2Eextreal_2Eextreal)
                 => ( p(ap(V0p,V2y))
                   => p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V2y)) ) )
              & ! [V3y] :
                  ( mem(V3y,ty_2Eextreal_2Eextreal)
                 => ( ! [V4z] :
                        ( mem(V4z,ty_2Eextreal_2Eextreal)
                       => ( p(ap(V0p,V4z))
                         => p(ap(ap(c_2Eextreal_2Eextreal__le,V3y),V4z)) ) )
                   => p(ap(ap(c_2Eextreal_2Eextreal__le,V3y),V1x)) ) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Einf__const,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(c_2Eextreal_2Eextreal__inf,f3367(V0x)) = V0x ) ).

fof(conj_thm_2Eextreal_2Einf__const__alt,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1z] :
          ( mem(V1z,ty_2Eextreal_2Eextreal)
         => ( ( ? [V2x] :
                  ( mem(V2x,ty_2Eextreal_2Eextreal)
                  & p(ap(V0p,V2x)) )
              & ! [V3x] :
                  ( mem(V3x,ty_2Eextreal_2Eextreal)
                 => ( p(ap(V0p,V3x))
                   => V3x = V1z ) ) )
           => ap(c_2Eextreal_2Eextreal__inf,V0p) = V1z ) ) ) ).

fof(conj_thm_2Eextreal_2Einf__const__over__set,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0s] :
          ( mem(V0s,arr(A_27a,bool))
         => ! [V1k] :
              ( mem(V1k,ty_2Eextreal_2Eextreal)
             => ( V0s != c_2Epred__set_2EEMPTY(A_27a)
               => ap(c_2Eextreal_2Eextreal__inf,ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Eextreal_2Eextreal),k(A_27a,V1k)),V0s)) = V1k ) ) ) ) ).

fof(conj_thm_2Eextreal_2Einf__suc,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ( ! [V1m] :
            ( mem(V1m,ty_2Enum_2Enum)
           => ! [V2n] :
                ( mem(V2n,ty_2Enum_2Enum)
               => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n))
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V0f,V2n)),ap(V0f,V1m))) ) ) )
       => ap(c_2Eextreal_2Eextreal__inf,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),f3370(V0f)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) = ap(c_2Eextreal_2Eextreal__inf,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) ) ) ).

fof(conj_thm_2Eextreal_2Einf__seq,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ! [V1l] :
          ( mem(V1l,ty_2Erealax_2Ereal)
         => ( p(ap(c_2Eextreal_2Emono__decreasing,V0f))
           => ( p(ap(ap(c_2Eseq_2E_2D_2D_3E,V0f),V1l))
            <=> ap(c_2Eextreal_2Eextreal__inf,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),f3371(V0f)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) = ap(c_2Eextreal_2ENormal,V1l) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Einf__lt__infty,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ( p(ap(ap(c_2Eextreal_2Eextreal__lt,c_2Eextreal_2ENegInf),ap(c_2Eextreal_2Eextreal__inf,V0p)))
       => ! [V1x] :
            ( mem(V1x,ty_2Eextreal_2Eextreal)
           => ( p(ap(V0p,V1x))
             => p(ap(ap(c_2Eextreal_2Eextreal__lt,c_2Eextreal_2ENegInf),V1x)) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Einf__min,axiom,
    ! [V0p] :
      ( mem(V0p,arr(ty_2Eextreal_2Eextreal,bool))
     => ! [V1z] :
          ( mem(V1z,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(V0p,V1z))
              & ! [V2x] :
                  ( mem(V2x,ty_2Eextreal_2Eextreal)
                 => ( p(ap(V0p,V2x))
                   => p(ap(ap(c_2Eextreal_2Eextreal__le,V1z),V2x)) ) ) )
           => ap(c_2Eextreal_2Eextreal__inf,V0p) = V1z ) ) ) ).

fof(lameq_f3377,axiom,
    ! [A_27a,V0f] :
      ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
     => ! [V1c] :
          ( mem(V1c,ty_2Erealax_2Ereal)
         => ! [V2n] : ap(f3377(A_27a,V0f,V1c),V2n) = ap(ap(c_2Eextreal_2Eextreal__sub,ap(c_2Eextreal_2ENormal,V1c)),ap(V0f,V2n)) ) ) ).

fof(conj_thm_2Eextreal_2Einf__cminus,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0f] :
          ( mem(V0f,arr(A_27a,ty_2Eextreal_2Eextreal))
         => ! [V1c] :
              ( mem(V1c,ty_2Erealax_2Ereal)
             => ap(ap(c_2Eextreal_2Eextreal__sub,ap(c_2Eextreal_2ENormal,V1c)),ap(c_2Eextreal_2Eextreal__inf,ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Eextreal_2Eextreal),V0f),c_2Epred__set_2EUNIV(A_27a)))) = ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Eextreal_2Eextreal),f3377(A_27a,V0f,V1c)),c_2Epred__set_2EUNIV(A_27a))) ) ) ) ).

fof(lameq_f3378,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1n] : ap(f3378(V0f),V1n) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Enum_2Enum),V0f),ap(c_2Epred__set_2Ecount,V1n)) ) ).

fof(ax_thm_2Eextreal_2Eext__suminf__def,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ap(c_2Eextreal_2Eext__suminf,V0f) = ap(c_2Eextreal_2Eextreal__sup,ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal),f3378(V0f)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) ) ).

fof(lameq_f3379,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1g] :
          ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
         => ! [V3n] : ap(f3379(V0f,V1g),V3n) = ap(ap(c_2Eextreal_2Eextreal__add,ap(V0f,V3n)),ap(V1g,V3n)) ) ) ).

fof(conj_thm_2Eextreal_2Eext__suminf__add,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1g] :
          ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
         => ( ! [V2n] :
                ( mem(V2n,ty_2Enum_2Enum)
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V0f,V2n)))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V1g,V2n))) ) )
           => ap(c_2Eextreal_2Eext__suminf,f3379(V0f,V1g)) = ap(ap(c_2Eextreal_2Eextreal__add,ap(c_2Eextreal_2Eext__suminf,V0f)),ap(c_2Eextreal_2Eext__suminf,V1g)) ) ) ) ).

fof(lameq_f3380,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1c] :
          ( mem(V1c,ty_2Eextreal_2Eextreal)
         => ! [V3n] : ap(f3380(V0f,V1c),V3n) = ap(ap(c_2Eextreal_2Eextreal__mul,V1c),ap(V0f,V3n)) ) ) ).

fof(conj_thm_2Eextreal_2Eext__suminf__cmul,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1c] :
          ( mem(V1c,ty_2Eextreal_2Eextreal)
         => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V1c))
              & ! [V2n] :
                  ( mem(V2n,ty_2Enum_2Enum)
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V0f,V2n))) ) )
           => ap(c_2Eextreal_2Eext__suminf,f3380(V0f,V1c)) = ap(ap(c_2Eextreal_2Eextreal__mul,V1c),ap(c_2Eextreal_2Eext__suminf,V0f)) ) ) ) ).

fof(lameq_f3381,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1c] :
          ( mem(V1c,ty_2Erealax_2Ereal)
         => ! [V4n] : ap(f3381(V0f,V1c),V4n) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V1c)),ap(V0f,V4n)) ) ) ).

fof(conj_thm_2Eextreal_2Eext__suminf__cmul__alt,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1c] :
          ( mem(V1c,ty_2Erealax_2Ereal)
         => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1c))
              & ( ! [V2n] :
                    ( mem(V2n,ty_2Enum_2Enum)
                   => ap(V0f,V2n) != c_2Eextreal_2ENegInf )
                | ! [V3n] :
                    ( mem(V3n,ty_2Enum_2Enum)
                   => ap(V0f,V3n) != c_2Eextreal_2EPosInf ) ) )
           => ap(c_2Eextreal_2Eext__suminf,f3381(V0f,V1c)) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V1c)),ap(c_2Eextreal_2Eext__suminf,V0f)) ) ) ) ).

fof(conj_thm_2Eextreal_2Eext__suminf__lt__infty,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ( ( ! [V1n] :
              ( mem(V1n,ty_2Enum_2Enum)
             => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V0f,V1n))) )
          & ap(c_2Eextreal_2Eext__suminf,V0f) != c_2Eextreal_2EPosInf )
       => ! [V2n] :
            ( mem(V2n,ty_2Enum_2Enum)
           => p(ap(ap(c_2Eextreal_2Eextreal__lt,ap(V0f,V2n)),c_2Eextreal_2EPosInf)) ) ) ) ).

fof(lameq_f3382,axiom,
    ! [V0r] :
      ( mem(V0r,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ! [V2n] : ap(f3382(V0r),V2n) = ap(c_2Eextreal_2ENormal,ap(V0r,V2n)) ) ).

fof(lameq_f3383,axiom,
    ! [V0r] :
      ( mem(V0r,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ! [V3n] : ap(f3383(V0r),V3n) = ap(c_2Eextreal_2ENormal,ap(V0r,V3n)) ) ).

fof(conj_thm_2Eextreal_2Eext__suminf__suminf,axiom,
    ! [V0r] :
      ( mem(V0r,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))
     => ( ( ! [V1n] :
              ( mem(V1n,ty_2Enum_2Enum)
             => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(V0r,V1n))) )
          & ap(c_2Eextreal_2Eext__suminf,f3382(V0r)) != c_2Eextreal_2EPosInf )
       => ap(c_2Eextreal_2Eext__suminf,f3383(V0r)) = ap(c_2Eextreal_2ENormal,ap(c_2Eseq_2Esuminf,V0r)) ) ) ).

fof(conj_thm_2Eextreal_2Eext__suminf__mono,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1g] :
          ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
         => ( ! [V2n] :
                ( mem(V2n,ty_2Enum_2Enum)
               => ( ap(V1g,V2n) != c_2Eextreal_2ENegInf
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V1g,V2n)),ap(V0f,V2n))) ) )
           => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eext__suminf,V1g)),ap(c_2Eextreal_2Eext__suminf,V0f))) ) ) ) ).

fof(lameq_f3384,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1g] :
          ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
         => ! [V3i] : ap(f3384(V0f,V1g),V3i) = ap(ap(c_2Eextreal_2Eextreal__sub,ap(V0f,V3i)),ap(V1g,V3i)) ) ) ).

fof(conj_thm_2Eextreal_2Eext__suminf__sub,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1g] :
          ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
         => ( ( ! [V2n] :
                  ( mem(V2n,ty_2Enum_2Enum)
                 => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V1g,V2n)))
                    & p(ap(ap(c_2Eextreal_2Eextreal__le,ap(V1g,V2n)),ap(V0f,V2n))) ) )
              & ap(c_2Eextreal_2Eext__suminf,V0f) != c_2Eextreal_2EPosInf )
           => ap(c_2Eextreal_2Eext__suminf,f3384(V0f,V1g)) = ap(ap(c_2Eextreal_2Eextreal__sub,ap(c_2Eextreal_2Eext__suminf,V0f)),ap(c_2Eextreal_2Eext__suminf,V1g)) ) ) ) ).

fof(conj_thm_2Eextreal_2Eext__suminf__sum,axiom,
    ! [V0f] :
      ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Eextreal_2Eextreal))
     => ! [V1n] :
          ( mem(V1n,ty_2Enum_2Enum)
         => ( ( ! [V2n] :
                  ( mem(V2n,ty_2Enum_2Enum)
                 => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V0f,V2n))) )
              & ! [V3m] :
                  ( mem(V3m,ty_2Enum_2Enum)
                 => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V3m))
                   => ap(V0f,V3m) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) ) ) )
           => ap(c_2Eextreal_2Eext__suminf,V0f) = ap(ap(c_2Eextreal_2EEXTREAL__SUM__IMAGE(ty_2Enum_2Enum),V0f),ap(c_2Epred__set_2Ecount,V1n)) ) ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__min__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__min,V0x),V1y) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)),V0x),V1y) ) ) ).

fof(ax_thm_2Eextreal_2Eextreal__max__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__max,V0x),V1y) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)),V1y),V0x) ) ) ).

fof(conj_thm_2Eextreal_2Emin__le,axiom,
    ! [V0z] :
      ( mem(V0z,ty_2Eextreal_2Eextreal)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__min,V1x),V2y)),V0z))
              <=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V0z))
                  | p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V0z)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Emin__le1,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__min,V0x),V1y)),V0x)) ) ) ).

fof(conj_thm_2Eextreal_2Emin__le2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__min,V0x),V1y)),V1y)) ) ) ).

fof(conj_thm_2Eextreal_2Ele__min,axiom,
    ! [V0z] :
      ( mem(V0z,ty_2Eextreal_2Eextreal)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0z),ap(ap(c_2Eextreal_2Eextreal__min,V1x),V2y)))
              <=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0z),V1x))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V0z),V2y)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Emin__le2__imp,axiom,
    ! [V0x1] :
      ( mem(V0x1,ty_2Eextreal_2Eextreal)
     => ! [V1x2] :
          ( mem(V1x2,ty_2Eextreal_2Eextreal)
         => ! [V2y1] :
              ( mem(V2y1,ty_2Eextreal_2Eextreal)
             => ! [V3y2] :
                  ( mem(V3y2,ty_2Eextreal_2Eextreal)
                 => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x1),V2y1))
                      & p(ap(ap(c_2Eextreal_2Eextreal__le,V1x2),V3y2)) )
                   => p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__min,V0x1),V1x2)),ap(ap(c_2Eextreal_2Eextreal__min,V2y1),V3y2))) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Emin__refl,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ap(ap(c_2Eextreal_2Eextreal__min,V0x),V0x) = V0x ) ).

fof(conj_thm_2Eextreal_2Emin__comm,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ap(ap(c_2Eextreal_2Eextreal__min,V0x),V1y) = ap(ap(c_2Eextreal_2Eextreal__min,V1y),V0x) ) ) ).

fof(conj_thm_2Eextreal_2Emin__infty,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ( ap(ap(c_2Eextreal_2Eextreal__min,V0x),c_2Eextreal_2EPosInf) = V0x
        & ap(ap(c_2Eextreal_2Eextreal__min,c_2Eextreal_2EPosInf),V0x) = V0x
        & ap(ap(c_2Eextreal_2Eextreal__min,c_2Eextreal_2ENegInf),V0x) = c_2Eextreal_2ENegInf
        & ap(ap(c_2Eextreal_2Eextreal__min,V0x),c_2Eextreal_2ENegInf) = c_2Eextreal_2ENegInf ) ) ).

fof(conj_thm_2Eextreal_2Ele__max,axiom,
    ! [V0z] :
      ( mem(V0z,ty_2Eextreal_2Eextreal)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0z),ap(ap(c_2Eextreal_2Eextreal__max,V1x),V2y)))
              <=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0z),V1x))
                  | p(ap(ap(c_2Eextreal_2Eextreal__le,V0z),V2y)) ) ) ) ) ) ).

fof(conj_thm_2Eextreal_2Ele__max1,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),ap(ap(c_2Eextreal_2Eextreal__max,V0x),V1y))) ) ) ).

fof(conj_thm_2Eextreal_2Ele__max2,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__max,V0x),V1y))) ) ) ).

fof(conj_thm_2Eextreal_2Emax__le,conjecture,
    ! [V0z] :
      ( mem(V0z,ty_2Eextreal_2Eextreal)
     => ! [V1x] :
          ( mem(V1x,ty_2Eextreal_2Eextreal)
         => ! [V2y] :
              ( mem(V2y,ty_2Eextreal_2Eextreal)
             => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,V1x),V2y)),V0z))
              <=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V0z))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V0z)) ) ) ) ) ) ).

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