ITP001 Axioms: ITP137+4.ax


%------------------------------------------------------------------------------
% File     : ITP137+4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : integral.ax [Gau19]
%          : HL4137+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  144 (  49 unt;   0 def)
%            Number of atoms       :  465 ( 122 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  328 (   7   ~;   5   |; 148   &)
%                                         (  27 <=>; 141  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   7 avg)
%            Maximal term depth    :   17 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  100 ( 100 usr;  53 con; 0-3 aty)
%            Number of variables   :  660 ( 633   !;  27   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0,V1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
      <=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
     => s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).

fof(reserved_2Eho_2Etruth,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).

fof(reserved_2Eho_2Enotfalse,axiom,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).

fof(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0] :
      ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).

fof(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).

fof(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        & p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        | p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
    <=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).

fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
       => p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a,V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
    <=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).

fof(reserved_2Equant_2E_21,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(reserved_2Equant_2E_3F,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        & p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        | p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
       => p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] :
      ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ereal_2Eabs_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2Eabs_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq1_2Ec_2Etransc_2Edsize_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Enum_2Enum),c_2Etransc_2Edsize_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X0_2E0))) ).

fof(arityeq1_2Ec_2Erealax_2Ereal__neg_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),c_2Ereal_2Ereal__of__num_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Elim_2Econtl_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elim_2Econtl_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Elim_2Econtl_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),c_2Epair_2E_2C_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Etransc_2Edivision_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)),c_2Etransc_2Edivision_2E0),s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0))) ).

fof(arityeq2_2Ec_2Etransc_2Efine_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool)),c_2Etransc_2Efine_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X1_2E0))) ).

fof(arityeq2_2Ec_2Etransc_2Egauge_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Etransc_2Egauge_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)),c_2Etransc_2Egauge_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))) ).

fof(arityeq2_2Ec_2Eintegral_2Eintegrable_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)),c_2Eintegral_2Eintegrable_2E0),s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))) ).

fof(arityeq2_2Ec_2Eintegral_2Eintegral_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal)),c_2Eintegral_2Eintegral_2E0),s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))) ).

fof(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Erealax_2Ereal__add_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Erealax_2Ereal__mul_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Etransc_2Ersum_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal)),c_2Etransc_2Ersum_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2Esum_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Esum_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal)),c_2Ereal_2Esum_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2Epow_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Ereal_2Epow_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Erealax_2Ereal__lt_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2Emin_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Emin_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Ereal_2Emin_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2Ereal__sub_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Ereal_2Ereal__sub_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Ereal_2Ereal__lte_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq1_2Ec_2Erealax_2Einv_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Einv_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Einv_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq2_2Ec_2Etransc_2Etdiv_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool)),c_2Etransc_2Etdiv_2E0),s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X1_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq3_2Ec_2Etransc_2EDint_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),c_2Etransc_2EDint_2E0),s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(arityeq3_2Ec_2Elim_2Ediffl_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Elim_2Ediffl_2E3(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),c_2Elim_2Ediffl_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(thm_2Eintegral_2Eintegrable__def,axiom,
    ! [V0a_2E0,V1b_2E0,V2f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0))))
    <=> ? [V3i_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0),s(tyop_2Erealax_2Ereal,V3i_2E0)))) ) ).

fof(thm_2Eintegral_2Eintegral__def,axiom,
    ! [F0_2E0] :
      ( ! [V0a_2E0,V1b_2E0,V2f_2E0,V3i_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0))),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0))),s(tyop_2Erealax_2Ereal,V3i_2E0))) = s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0),s(tyop_2Erealax_2Ereal,V3i_2E0)))
     => ! [V0a_2E0,V1b_2E0,V2f_2E0] : s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0))) = s(tyop_2Erealax_2Ereal,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0))),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0))))) ) ).

fof(thm_2Eintegral_2ESUM__SPLIT,axiom,
    ! [V0m_2E0,V1f_2E0,V2n_2E0,V3p_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Esum_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1f_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Esum_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V3p_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1f_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Esum_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3p_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1f_2E0))) ).

fof(thm_2Eintegral_2EDIVISION__APPEND__EXPLICIT,axiom,
    ! [F2_2E0,F1_2E0,F0_2E0,F5_2E0,F4_2E0,F3_2E0] :
      ( ! [V4d1_2E0,V6d2_2E0,V13n_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0))),s(tyop_2Enum_2Enum,V13n_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V13n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0),s(tyop_2Enum_2Enum,V13n_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V13n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0)))))))))
     => ( ! [V4d1_2E0,V6d2_2E0,V10n_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0))),s(tyop_2Enum_2Enum,V10n_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0),s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0)))))))))
       => ( ! [V4d1_2E0,V6d2_2E0,V8n_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0))),s(tyop_2Enum_2Enum,V8n_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V8n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0),s(tyop_2Enum_2Enum,V8n_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V8n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0)))))))))
         => ( ! [V4d1_2E0,V5p1_2E0,V7p2_2E0,V14n_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))),F5_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))),s(tyop_2Enum_2Enum,V14n_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V14n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0),s(tyop_2Enum_2Enum,V14n_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V14n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0)))))))))
           => ( ! [V4d1_2E0,V5p1_2E0,V7p2_2E0,V11n_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))),F4_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))),s(tyop_2Enum_2Enum,V11n_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V11n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0),s(tyop_2Enum_2Enum,V11n_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V11n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0)))))))))
             => ( ! [V4d1_2E0,V5p1_2E0,V7p2_2E0,V9n_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))),s(tyop_2Enum_2Enum,V9n_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V9n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0),s(tyop_2Enum_2Enum,V9n_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V9n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0)))))))))
               => ! [V0a_2E0,V1b_2E0,V2c_2E0,V3g_2E0,V4d1_2E0,V5p1_2E0,V6d2_2E0,V7p2_2E0] :
                    ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))))))
                      & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))))))
                      & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1b_2E0),s(tyop_2Erealax_2Ereal,V2c_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))))))
                      & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0)))))) )
                   => ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V2c_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))))))))
                      & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))),F4_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))))))))
                      & ! [V12f_2E0] : s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))),F5_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V12f_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4d1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V12f_2E0))),s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V12f_2E0))))) ) ) ) ) ) ) ) ) ).

fof(thm_2Eintegral_2EDIVISION__APPEND__STRONG,axiom,
    ! [V0g_2E0,V1a_2E0,V2b_2E0,V3c_2E0,V4D1_2E0,V5p1_2E0,V6D2_2E0,V7p2_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4D1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4D1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6D2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6D2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0)))))) )
     => ? [V8D_2E0,V9p_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8D_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p_2E0))))))
          & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8D_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p_2E0))))))
          & ! [V10f_2E0] : s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8D_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V10f_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4D1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V10f_2E0))),s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6D2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V10f_2E0))))) ) ) ).

fof(thm_2Eintegral_2EDIVISION__APPEND,axiom,
    ! [V0g_2E0,V1a_2E0,V2b_2E0,V3c_2E0] :
      ( ( ? [V4D1_2E0,V5p1_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4D1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))))))
            & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4D1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0)))))) )
        & ? [V6D2_2E0,V7p2_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6D2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))))))
            & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6D2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0)))))) ) )
     => ? [V8D_2E0,V9p_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8D_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p_2E0))))))
          & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8D_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__DINT,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))))) ) ).

fof(thm_2Eintegral_2EDIVISION__BOUNDS,axiom,
    ! [V0d_2E0,V1a_2E0,V2b_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0))))
     => ! [V3n_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))
          & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Erealax_2Ereal,V2b_2E0)))) ) ) ).

fof(thm_2Eintegral_2ETDIV__BOUNDS,axiom,
    ! [V0d_2E0,V1p_2E0,V2a_2E0,V3b_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1p_2E0))))))
     => ! [V4n_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))
          & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Erealax_2Ereal,V3b_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1p_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))
          & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1p_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Erealax_2Ereal,V3b_2E0)))) ) ) ).

fof(thm_2Eintegral_2ETDIV__LE,axiom,
    ! [V0d_2E0,V1p_2E0,V2a_2E0,V3b_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1p_2E0))))))
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0)))) ) ).

fof(thm_2Eintegral_2EDINT__WRONG,axiom,
    ! [V0a_2E0,V1b_2E0,V2f_2E0,V3i_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1b_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0),s(tyop_2Erealax_2Ereal,V3i_2E0)))) ) ).

fof(thm_2Eintegral_2EDINT__INTEGRAL,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0,V3i_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V3i_2E0)))) )
     => s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))) = s(tyop_2Erealax_2Ereal,V3i_2E0) ) ).

fof(thm_2Eintegral_2EDINT__NEG,axiom,
    ! [F0_2E0] :
      ( ! [V0f_2E0,V4x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,V4x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0)))))
     => ! [V0f_2E0,V1a_2E0,V2b_2E0,V3i_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V3i_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,V3i_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EDINT__0,axiom,
    ! [F0_2E0] :
      ( ! [V2x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),F0_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
     => ! [V0a_2E0,V1b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),F0_2E0),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) ) ).

fof(thm_2Eintegral_2EDINT__ADD,axiom,
    ! [F0_2E0] :
      ( ! [V0f_2E0,V1g_2E0,V6x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Erealax_2Ereal,V6x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0)))))
     => ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0,V4i_2E0,V5j_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4i_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V5j_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,V4i_2E0),s(tyop_2Erealax_2Ereal,V5j_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EDINT__SUB,axiom,
    ! [F0_2E0] :
      ( ! [V0f_2E0,V1g_2E0,V6x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Erealax_2Ereal,V6x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0)))))
     => ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0,V4i_2E0,V5j_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4i_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V5j_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V4i_2E0),s(tyop_2Erealax_2Ereal,V5j_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EDSIZE__EQ,axiom,
    ! [F0_2E0] :
      ( ! [V2D_2E0,V3n_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2D_2E0))),s(tyop_2Enum_2Enum,V3n_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2D_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2D_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))
     => ! [V0a_2E0,V1b_2E0,V2D_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2D_2E0))))
         => s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Esum_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2D_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2D_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V1b_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ) ).

fof(thm_2Eintegral_2EDINT__CONST,axiom,
    ! [F0_2E0] :
      ( ! [V2c_2E0,V3x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V2c_2E0))),s(tyop_2Erealax_2Ereal,V3x_2E0))) = s(tyop_2Erealax_2Ereal,V2c_2E0)
     => ! [V0a_2E0,V1b_2E0,V2c_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V2c_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V2c_2E0),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V1b_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0)))))))) ) ).

fof(thm_2Eintegral_2EDINT__CMUL,axiom,
    ! [F0_2E0] :
      ( ! [V3c_2E0,V0f_2E0,V5x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,V5x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0)))))
     => ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0,V4i_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4i_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,V4i_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EDINT__LINEAR,axiom,
    ! [F0_2E0] :
      ( ! [V1m_2E0,V2f_2E0,V0n_2E0,V3g_2E0,V8x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))))),F0_2E0),s(tyop_2Erealax_2Ereal,V1m_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0))),s(tyop_2Erealax_2Ereal,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_2E0))),s(tyop_2Erealax_2Ereal,V8x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V1m_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0),s(tyop_2Erealax_2Ereal,V8x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V0n_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_2E0),s(tyop_2Erealax_2Ereal,V8x_2E0)))))))
     => ! [V0n_2E0,V1m_2E0,V2f_2E0,V3g_2E0,V4a_2E0,V5b_2E0,V6i_2E0,V7j_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0),s(tyop_2Erealax_2Ereal,V6i_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_2E0),s(tyop_2Erealax_2Ereal,V7j_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))))),F0_2E0),s(tyop_2Erealax_2Ereal,V1m_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_2E0))),s(tyop_2Erealax_2Ereal,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V1m_2E0),s(tyop_2Erealax_2Ereal,V6i_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V0n_2E0),s(tyop_2Erealax_2Ereal,V7j_2E0)))))))) ) ) ).

fof(thm_2Eintegral_2ELT,axiom,
    ( ! [V0m_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
    & ! [V1m_2E0,V2n_2E0] :
        ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))))
      <=> ( s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,V2n_2E0)
          | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) ) ) ) ).

fof(thm_2Eintegral_2ELE__0,axiom,
    ! [V0n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) ).

fof(thm_2Eintegral_2ELT__0,axiom,
    ! [V0n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) ).

fof(thm_2Eintegral_2EEQ__SUC,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))
    <=> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) ) ).

fof(thm_2Eintegral_2ELE__LT,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))
        | s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) ) ) ).

fof(thm_2Eintegral_2ELT__LE,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))
        & s(tyop_2Enum_2Enum,V0m_2E0) != s(tyop_2Enum_2Enum,V1n_2E0) ) ) ).

fof(thm_2Eintegral_2EREAL__LT__MIN,axiom,
    ! [V0x_2E0,V1y_2E0,V2z_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V2z_2E0),s(tyop_2Erealax_2Ereal,c_2Ereal_2Emin_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1y_2E0))))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V2z_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V2z_2E0),s(tyop_2Erealax_2Ereal,V1y_2E0)))) ) ) ).

fof(thm_2Eintegral_2EREAL__LE__RMUL1,axiom,
    ! [V0x_2E0,V1y_2E0,V2z_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1y_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V2z_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V2z_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V1y_2E0),s(tyop_2Erealax_2Ereal,V2z_2E0)))))) ) ).

fof(thm_2Eintegral_2EREAL__LE__LMUL1,axiom,
    ! [V0x_2E0,V1y_2E0,V2z_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V0x_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1y_2E0),s(tyop_2Erealax_2Ereal,V2z_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1y_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V2z_2E0)))))) ) ).

fof(thm_2Eintegral_2EINTEGRAL__LE,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0,V4i_2E0,V5j_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))))
        & ! [V6x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0)))))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0)))))) ) ).

fof(thm_2Eintegral_2EDINT__LE,axiom,
    ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0,V4i_2E0,V5j_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4i_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V5j_2E0))))
        & ! [V6x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0)))))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4i_2E0),s(tyop_2Erealax_2Ereal,V5j_2E0)))) ) ).

fof(thm_2Eintegral_2EDINT__TRIANGLE,axiom,
    ! [F0_2E0] :
      ( ! [V0f_2E0,V5x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,V5x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0)))))
     => ! [V0f_2E0,V1a_2E0,V2b_2E0,V3i_2E0,V4j_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V3i_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,V4j_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V3i_2E0))),s(tyop_2Erealax_2Ereal,V4j_2E0)))) ) ) ).

fof(thm_2Eintegral_2EDINT__EQ,axiom,
    ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0,V4i_2E0,V5j_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4i_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V5j_2E0))))
        & ! [V6x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0)))) )
           => s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))) ) )
     => s(tyop_2Erealax_2Ereal,V4i_2E0) = s(tyop_2Erealax_2Ereal,V5j_2E0) ) ).

fof(thm_2Eintegral_2EINTEGRAL__EQ,axiom,
    ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0,V4i_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4i_2E0))))
        & ! [V5x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V5x_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0)))) )
           => s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V4i_2E0)))) ) ).

fof(thm_2Eintegral_2EINTEGRATION__BY__PARTS,axiom,
    ! [F0_2E0] :
      ( ! [V2f_27_2E0,V1g_2E0,V0f_2E0,V3g_27_2E0,V8x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0))),s(tyop_2Erealax_2Ereal,V8x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0),s(tyop_2Erealax_2Ereal,V8x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V8x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V8x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0),s(tyop_2Erealax_2Ereal,V8x_2E0)))))))
     => ! [V0f_2E0,V1g_2E0,V2f_27_2E0,V3g_27_2E0,V4a_2E0,V5b_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))))
            & ! [V6x_2E0] :
                ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
                  & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0)))) )
               => p(s(tyop_2Emin_2Ebool,c_2Elim_2Ediffl_2E3(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))),s(tyop_2Erealax_2Ereal,V6x_2E0)))) )
            & ! [V7x_2E0] :
                ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V7x_2E0))))
                  & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V7x_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0)))) )
               => p(s(tyop_2Emin_2Ebool,c_2Elim_2Ediffl_2E3(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0),s(tyop_2Erealax_2Ereal,V7x_2E0))),s(tyop_2Erealax_2Ereal,V7x_2E0)))) ) )
         => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4a_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V4a_2E0)))))))))) ) ) ).

fof(thm_2Eintegral_2EDIVISION__LE__SUC,axiom,
    ! [V0d_2E0,V1a_2E0,V2b_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0))))
     => ! [V3n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))))) ) ).

fof(thm_2Eintegral_2EDIVISION__MONO__LE,axiom,
    ! [V0d_2E0,V1a_2E0,V2b_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0))))
     => ! [V3m_2E0,V4n_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,V3m_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EDIVISION__MONO__LE__SUC,axiom,
    ! [V0d_2E0,V1a_2E0,V2b_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0))))
     => ! [V3n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))))) ) ).

fof(thm_2Eintegral_2EDIVISION__DSIZE__LE,axiom,
    ! [V0a_2E0,V1b_2E0,V2d_2E0,V3n_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0))))
        & s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,V3n_2E0))) )
     => p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0))),s(tyop_2Enum_2Enum,V3n_2E0)))) ) ).

fof(thm_2Eintegral_2EDIVISION__DSIZE__GE,axiom,
    ! [V0a_2E0,V1b_2E0,V2d_2E0,V3n_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))))) )
     => p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0)))))) ) ).

fof(thm_2Eintegral_2EDIVISION__DSIZE__EQ,axiom,
    ! [V0a_2E0,V1b_2E0,V2d_2E0,V3n_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))))
        & s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))) )
     => s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))) ) ).

fof(thm_2Eintegral_2EDIVISION__DSIZE__EQ__ALT,axiom,
    ! [V0a_2E0,V1b_2E0,V2d_2E0,V3n_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0))))
        & s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))
        & ! [V4i_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))
           => p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,V4i_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4i_2E0)))))))) ) )
     => s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0))) = s(tyop_2Enum_2Enum,V3n_2E0) ) ).

fof(thm_2Eintegral_2Enum__MAX,axiom,
    ! [V0P_2E0] :
      ( ( ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))
        & ? [V2M_2E0] :
          ! [V3x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3x_2E0))))
           => p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V2M_2E0)))) ) )
    <=> ? [V4m_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V4m_2E0))))
          & ! [V5x_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V5x_2E0))))
             => p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V5x_2E0),s(tyop_2Enum_2Enum,V4m_2E0)))) ) ) ) ).

fof(thm_2Eintegral_2EDIVISION__INTERMEDIATE,axiom,
    ! [V0d_2E0,V1a_2E0,V2b_2E0,V3c_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Edivision_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0)))) )
     => ? [V4n_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Etransc_2Edsize_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0))))))
          & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Erealax_2Ereal,V3c_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))))))) ) ) ).

fof(thm_2Eintegral_2EDINT__COMBINE,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0,V4i_2E0,V5j_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4i_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V5j_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,V4i_2E0),s(tyop_2Erealax_2Ereal,V5j_2E0)))))) ) ).

fof(thm_2Eintegral_2ESUM__EQ__0,axiom,
    ! [V0n_2E0,V1m_2E0,V2f_2E0] :
      ( ! [V3r_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V3r_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) )
         => s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2f_2E0),s(tyop_2Enum_2Enum,V3r_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => s(tyop_2Erealax_2Ereal,c_2Ereal_2Esum_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2f_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ).

fof(thm_2Eintegral_2EDINT__DELTA__LEFT,axiom,
    ! [F1_2E0,F0_2E0] :
      ( ! [V2x_2E0,V0a_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))),s(tyop_2Erealax_2Ereal,V0a_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V2x_2E0) = s(tyop_2Erealax_2Ereal,V0a_2E0) )
     => ( ! [V0a_2E0,V2x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))),s(tyop_2Erealax_2Ereal,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))
       => ! [V0a_2E0,V1b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EDINT__DELTA__RIGHT,axiom,
    ! [F1_2E0,F0_2E0] :
      ( ! [V2x_2E0,V1b_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))),s(tyop_2Erealax_2Ereal,V1b_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V2x_2E0) = s(tyop_2Erealax_2Ereal,V1b_2E0) )
     => ( ! [V1b_2E0,V2x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))
       => ! [V0a_2E0,V1b_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EDINT__DELTA,axiom,
    ! [F1_2E0,F0_2E0] :
      ( ! [V3x_2E0,V2c_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0))),s(tyop_2Erealax_2Ereal,V2c_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V3x_2E0) = s(tyop_2Erealax_2Ereal,V2c_2E0) )
     => ( ! [V2c_2E0,V3x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V2c_2E0))),s(tyop_2Erealax_2Ereal,V3x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0))),s(tyop_2Erealax_2Ereal,V2c_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))
       => ! [V0a_2E0,V1b_2E0,V2c_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V2c_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EDINT__POINT__SPIKE,axiom,
    ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0,V4c_2E0,V5i_2E0] :
      ( ( ! [V6x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))))
              & s(tyop_2Erealax_2Ereal,V6x_2E0) != s(tyop_2Erealax_2Ereal,V4c_2E0) )
           => s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))) )
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V5i_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V5i_2E0)))) ) ).

fof(thm_2Eintegral_2EDINT__FINITE__SPIKE,axiom,
    ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0,V4s_2E0,V5i_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V4s_2E0))))
        & ! [V6x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))))
              & ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V4s_2E0)))) )
           => s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))) )
        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V5i_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etransc_2EDint_2E3(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V5i_2E0)))) ) ).

fof(thm_2Eintegral_2EREAL__POW__LBOUND,axiom,
    ! [V0x_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V0x_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Erealax_2Ereal,V0x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V0x_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) ) ).

fof(thm_2Eintegral_2EREAL__ARCH__POW,axiom,
    ! [V0x_2E0,V1y_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V0x_2E0))))
     => ? [V2n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1y_2E0),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) ) ).

fof(thm_2Eintegral_2EREAL__ARCH__POW2,axiom,
    ! [V0x_2E0] :
    ? [V1n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V1n_2E0)))))) ).

fof(thm_2Eintegral_2EREAL__POW__LE__1,axiom,
    ! [V0n_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) ) ).

fof(thm_2Eintegral_2EREAL__POW__MONO,axiom,
    ! [V0m_2E0,V1n_2E0,V2x_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V2x_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,V2x_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,V2x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) ) ).

fof(thm_2Eintegral_2EREAL__LE__INV2,axiom,
    ! [V0x_2E0,V1y_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V0x_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1y_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Einv_2E1(s(tyop_2Erealax_2Ereal,V1y_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Einv_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0)))))) ) ).

fof(thm_2Eintegral_2EGAUGE__MIN__FINITE,axiom,
    ! [V0s_2E0,V1gs_2E0,V2n_2E0] :
      ( ! [V3m_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Etransc_2Egauge_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),V1gs_2E0),s(tyop_2Enum_2Enum,V3m_2E0)))))) )
     => ? [V4g_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Egauge_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V4g_2E0))))
          & ! [V5d_2E0,V6p_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V4g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5d_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6p_2E0))))))
             => ! [V7m_2E0] :
                  ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V7m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))
                 => p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),V1gs_2E0),s(tyop_2Enum_2Enum,V7m_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5d_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6p_2E0)))))) ) ) ) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__CAUCHY,axiom,
    ! [F0_2E0] :
      ( ! [V1a_2E0,V2b_2E0,V5x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Erealax_2Ereal,V1a_2E0))),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Erealax_2Ereal,V5x_2E0))))
        <=> ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V5x_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0)))) ) )
     => ! [V0f_2E0,V1a_2E0,V2b_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))
        <=> ! [V3e_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V3e_2E0))))
             => ? [V4g_2E0] :
                  ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Egauge_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Erealax_2Ereal,V1a_2E0))),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V4g_2E0))))
                  & ! [V6d1_2E0,V7p1_2E0,V8d2_2E0,V9p2_2E0] :
                      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p1_2E0))))))
                        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V4g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p1_2E0))))))
                        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8d2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p2_2E0))))))
                        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V4g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8d2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p2_2E0)))))) )
                     => p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6d1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8d2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p2_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))))),s(tyop_2Erealax_2Ereal,V3e_2E0)))) ) ) ) ) ) ).

fof(thm_2Eintegral_2ESUM__DIFFS,axiom,
    ! [F0_2E0] :
      ( ! [V0f_2E0,V3n_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Enum_2Enum,V3n_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))
     => ! [V0f_2E0,V1n_2E0,V2d_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Esum_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0f_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2d_2E0))))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) ) ).

fof(thm_2Eintegral_2ERSUM__BOUND,axiom,
    ! [V0a_2E0,V1b_2E0,V2d_2E0,V3p_2E0,V4e_2E0,V5f_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V3p_2E0))))))
        & ! [V6x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V5f_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))),s(tyop_2Erealax_2Ereal,V4e_2E0)))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V3p_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V5f_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V4e_2E0),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V1b_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0)))))))) ) ).

fof(thm_2Eintegral_2ERSUM__DIFF__BOUND,axiom,
    ! [V0a_2E0,V1b_2E0,V2d_2E0,V3p_2E0,V4e_2E0,V5f_2E0,V6g_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V3p_2E0))))))
        & ! [V7x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V7x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V7x_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V5f_2E0),s(tyop_2Erealax_2Ereal,V7x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V6g_2E0),s(tyop_2Erealax_2Ereal,V7x_2E0))))))),s(tyop_2Erealax_2Ereal,V4e_2E0)))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V3p_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V5f_2E0))),s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2d_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V3p_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V6g_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V4e_2E0),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V1b_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0)))))))) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__LIMIT,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0] :
      ( ! [V3e_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V3e_2E0))))
         => ? [V4g_2E0] :
              ( ! [V5x_2E0] :
                  ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0))))
                    & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V5x_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0)))) )
                 => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V4g_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0))))))),s(tyop_2Erealax_2Ereal,V3e_2E0)))) )
              & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V4g_2E0)))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__CONST,axiom,
    ! [F0_2E0] :
      ( ! [V2c_2E0,V3x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V2c_2E0))),s(tyop_2Erealax_2Ereal,V3x_2E0))) = s(tyop_2Erealax_2Ereal,V2c_2E0)
     => ! [V0a_2E0,V1b_2E0,V2c_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V2c_2E0)))))) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__ADD,axiom,
    ! [F0_2E0] :
      ( ! [V0f_2E0,V1g_2E0,V4x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Erealax_2Ereal,V4x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0)))))
     => ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__CMUL,axiom,
    ! [F0_2E0] :
      ( ! [V3c_2E0,V0f_2E0,V4x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,V4x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0)))))
     => ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))))) ) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__COMBINE,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__POINT__SPIKE,axiom,
    ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0,V4c_2E0] :
      ( ( ! [V5x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V5x_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))))
              & s(tyop_2Erealax_2Ereal,V5x_2E0) != s(tyop_2Erealax_2Ereal,V4c_2E0) )
           => s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V5x_2E0))) )
        & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0)))) ) ).

fof(thm_2Eintegral_2ESUP__INTERVAL,axiom,
    ! [V0P_2E0,V1a_2E0,V2b_2E0] :
      ( ? [V3x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V3x_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
          & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0)))) )
     => ? [V4s_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V4s_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4s_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
          & ! [V5y_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V5y_2E0),s(tyop_2Erealax_2Ereal,V4s_2E0))))
            <=> ? [V6x_2E0] :
                  ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
                  & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
                  & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
                  & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V5y_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0)))) ) ) ) ) ).

fof(thm_2Eintegral_2EBOLZANO__LEMMA__ALT,axiom,
    ! [V0P_2E0] :
      ( ( ! [V1a_2E0,V2b_2E0,V3c_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Erealax_2Ereal,V1a_2E0))),s(tyop_2Erealax_2Ereal,V2b_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Erealax_2Ereal,V3c_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Erealax_2Ereal,V1a_2E0))),s(tyop_2Erealax_2Ereal,V3c_2E0)))) )
        & ! [V4x_2E0] :
          ? [V5d_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V5d_2E0))))
            & ! [V6a_2E0,V7b_2E0] :
                ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6a_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0))))
                  & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4x_2E0),s(tyop_2Erealax_2Ereal,V7b_2E0))))
                  & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V7b_2E0),s(tyop_2Erealax_2Ereal,V6a_2E0))),s(tyop_2Erealax_2Ereal,V5d_2E0)))) )
               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Erealax_2Ereal,V6a_2E0))),s(tyop_2Erealax_2Ereal,V7b_2E0)))) ) ) )
     => ! [V8a_2E0,V9b_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V8a_2E0),s(tyop_2Erealax_2Ereal,V9b_2E0))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Erealax_2Ereal,V8a_2E0))),s(tyop_2Erealax_2Ereal,V9b_2E0)))) ) ) ).

fof(thm_2Eintegral_2ECONT__UNIFORM,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
        & ! [V3x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V3x_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,c_2Elim_2Econtl_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0)))) ) )
     => ! [V4e_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V4e_2E0))))
         => ? [V5d_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V5d_2E0))))
              & ! [V6x_2E0,V7y_2E0] :
                  ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
                    & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
                    & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V7y_2E0))))
                    & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V7y_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
                    & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V7y_2E0))))),s(tyop_2Erealax_2Ereal,V5d_2E0)))) )
                 => p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V7y_2E0))))))),s(tyop_2Erealax_2Ereal,V4e_2E0)))) ) ) ) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__CONTINUOUS,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0] :
      ( ! [V3x_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V3x_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Elim_2Econtl_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__SPLIT__SIDES,axiom,
    ! [F0_2E0] :
      ( ! [V1a_2E0,V2b_2E0,V7x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Erealax_2Ereal,V1a_2E0))),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Erealax_2Ereal,V7x_2E0))))
        <=> ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V7x_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V7x_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0)))) ) )
     => ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) )
         => ? [V4i_2E0] :
            ! [V5e_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V5e_2E0))))
             => ? [V6g_2E0] :
                  ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Egauge_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Erealax_2Ereal,V1a_2E0))),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V6g_2E0))))
                  & ! [V8d1_2E0,V9p1_2E0,V10d2_2E0,V11p2_2E0] :
                      ( ( p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8d1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p1_2E0))))))
                        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V6g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8d1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p1_2E0))))))
                        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V10d2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V11p2_2E0))))))
                        & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V6g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V10d2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V11p2_2E0)))))) )
                     => p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8d1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V10d2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V11p2_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))),s(tyop_2Erealax_2Ereal,V4i_2E0))))),s(tyop_2Erealax_2Ereal,V5e_2E0)))) ) ) ) ) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__SUBINTERVAL__LEFT,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__SUBINTERVAL__RIGHT,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) ) ).

fof(thm_2Eintegral_2EINTEGRABLE__SUBINTERVAL,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0,V4d_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,V4d_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4d_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V3c_2E0),s(tyop_2Erealax_2Ereal,V4d_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) ) ).

fof(thm_2Eintegral_2EINTEGRAL__0,axiom,
    ! [F0_2E0] :
      ( ! [V2x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),F0_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
     => ! [V0a_2E0,V1b_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))))
         => s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),F0_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ) ).

fof(thm_2Eintegral_2EINTEGRAL__CONST,axiom,
    ! [F0_2E0] :
      ( ! [V2c_2E0,V3x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V2c_2E0))),s(tyop_2Erealax_2Ereal,V3x_2E0))) = s(tyop_2Erealax_2Ereal,V2c_2E0)
     => ! [V0a_2E0,V1b_2E0,V2c_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))))
         => s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Erealax_2Ereal,V2c_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V2c_2E0),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V1b_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0))))) ) ) ).

fof(thm_2Eintegral_2EINTEGRAL__CMUL,axiom,
    ! [F0_2E0] :
      ( ! [V1c_2E0,V0f_2E0,V4x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Erealax_2Ereal,V1c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,V4x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V1c_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0)))))
     => ! [V0f_2E0,V1c_2E0,V2a_2E0,V3b_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) )
         => s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Erealax_2Ereal,V1c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V1c_2E0),s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))) ) ) ).

fof(thm_2Eintegral_2EINTEGRAL__ADD,axiom,
    ! [F0_2E0] :
      ( ! [V0f_2E0,V1g_2E0,V4x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Erealax_2Ereal,V4x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0)))))
     => ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0)))) )
         => s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))))) ) ) ).

fof(thm_2Eintegral_2EINTEGRAL__SUB,axiom,
    ! [F0_2E0] :
      ( ! [V0f_2E0,V1g_2E0,V4x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Erealax_2Ereal,V4x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0)))))
     => ! [V0f_2E0,V1g_2E0,V2a_2E0,V3b_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0)))) )
         => s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2a_2E0),s(tyop_2Erealax_2Ereal,V3b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))))) ) ) ).

fof(thm_2Eintegral_2EINTEGRAL__BY__PARTS,axiom,
    ! [F3_2E0,F2_2E0,F1_2E0,F0_2E0] :
      ( ! [V2f_27_2E0,V1g_2E0,V11x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Erealax_2Ereal,V11x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0),s(tyop_2Erealax_2Ereal,V11x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V11x_2E0)))))
     => ( ! [V0f_2E0,V3g_27_2E0,V10x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0))),s(tyop_2Erealax_2Ereal,V10x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V10x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0),s(tyop_2Erealax_2Ereal,V10x_2E0)))))
       => ( ! [V0f_2E0,V3g_27_2E0,V9x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0))),s(tyop_2Erealax_2Ereal,V9x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V9x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0),s(tyop_2Erealax_2Ereal,V9x_2E0)))))
         => ( ! [V2f_27_2E0,V1g_2E0,V8x_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))),s(tyop_2Erealax_2Ereal,V8x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0),s(tyop_2Erealax_2Ereal,V8x_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V8x_2E0)))))
           => ! [V0f_2E0,V1g_2E0,V2f_27_2E0,V3g_27_2E0,V4a_2E0,V5b_2E0] :
                ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))))
                  & ! [V6x_2E0] :
                      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))))
                        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V6x_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0)))) )
                     => p(s(tyop_2Emin_2Ebool,c_2Elim_2Ediffl_2E3(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0),s(tyop_2Erealax_2Ereal,V6x_2E0))),s(tyop_2Erealax_2Ereal,V6x_2E0)))) )
                  & ! [V7x_2E0] :
                      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V7x_2E0))))
                        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V7x_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0)))) )
                     => p(s(tyop_2Emin_2Ebool,c_2Elim_2Ediffl_2E3(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0),s(tyop_2Erealax_2Ereal,V7x_2E0))),s(tyop_2Erealax_2Ereal,V7x_2E0)))) )
                  & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))))))
                  & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0)))))) )
               => s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V3g_27_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4a_2E0))),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0),s(tyop_2Erealax_2Ereal,V4a_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Erealax_2Ereal,V5b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V2f_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V1g_2E0))))))) ) ) ) ) ) ).

fof(thm_2Eintegral_2EINTEGRAL__COMBINE,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eintegral_2Eintegrable_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0)))) )
     => s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))))) ) ).

fof(thm_2Eintegral_2EINTEGRAL__MVT1,axiom,
    ! [V0f_2E0,V1a_2E0,V2b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
        & ! [V3x_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V3x_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,c_2Elim_2Econtl_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0)))) ) )
     => ? [V4x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V4x_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))))
          & s(tyop_2Erealax_2Ereal,c_2Eintegral_2Eintegral_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Erealax_2Ereal,V4x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V1a_2E0))))) ) ) ).

fof(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
     => s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).

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