SET007 Axioms: SET007+835.ax


%------------------------------------------------------------------------------
% File     : SET007+835 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Uniform Continuity of Functions on Normed Linear Spaces
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : nfcont_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   21 (   0 unit)
%            Number of atoms       :  406 (   9 equality)
%            Maximal formula depth :   27 (  15 average)
%            Number of connectives :  442 (  57 ~  ;   0  |; 291  &)
%                                         (   3 <=>;  91 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   0 propositional; 1-4 arity)
%            Number of functors    :   27 (   5 constant; 0-4 arity)
%            Number of variables   :   95 (   0 singleton;  92 !;   3 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(d1_nfcont_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v7_rlvect_1(C)
            & v2_normsp_1(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
             => ( r1_nfcont_2(A,B,C,D)
              <=> ( r1_tarski(A,k4_relset_1(u1_struct_0(B),u1_struct_0(C),D))
                  & ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ~ ( ~ r1_xreal_0(E,np__0)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ~ ( ~ r1_xreal_0(F,np__0)
                                  & ! [G] :
                                      ( m1_subset_1(G,u1_struct_0(B))
                                     => ! [H] :
                                          ( m1_subset_1(H,u1_struct_0(B))
                                         => ~ ( r2_hidden(G,A)
                                              & r2_hidden(H,A)
                                              & ~ r1_xreal_0(F,k1_normsp_1(B,k6_rlvect_1(B,G,H)))
                                              & r1_xreal_0(E,k1_normsp_1(C,k6_rlvect_1(C,k4_finseq_4(u1_struct_0(B),u1_struct_0(C),D,G),k4_finseq_4(u1_struct_0(B),u1_struct_0(C),D,H)))) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_nfcont_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,u1_struct_0(B),k1_numbers) )
         => ( r2_nfcont_2(A,B,C)
          <=> ( r1_tarski(A,k4_relset_1(u1_struct_0(B),k1_numbers,C))
              & ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ~ ( ~ r1_xreal_0(D,np__0)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(E,np__0)
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(B))
                                 => ! [G] :
                                      ( m1_subset_1(G,u1_struct_0(B))
                                     => ~ ( r2_hidden(F,A)
                                          & r2_hidden(G,A)
                                          & ~ r1_xreal_0(E,k1_normsp_1(B,k6_rlvect_1(B,F,G)))
                                          & r1_xreal_0(D,k18_complex1(k5_real_1(k4_finseq_4(u1_struct_0(B),k1_numbers,C,F),k4_finseq_4(u1_struct_0(B),k1_numbers,C,G)))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t1_nfcont_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v7_rlvect_1(C)
        & v2_normsp_1(C)
        & l1_normsp_1(C) )
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
             => ( ( r1_nfcont_2(A,C,D,E)
                  & r1_tarski(B,A) )
               => r1_nfcont_2(B,C,D,E) ) ) ) ) )).

fof(t2_nfcont_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v7_rlvect_1(C)
        & v2_normsp_1(C)
        & l1_normsp_1(C) )
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                 => ( ( r1_nfcont_2(A,C,D,E)
                      & r1_nfcont_2(B,C,D,F) )
                   => r1_nfcont_2(k3_xboole_0(A,B),C,D,k1_vfunct_1(u1_struct_0(C),D,E,F)) ) ) ) ) ) )).

fof(t3_nfcont_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v7_rlvect_1(C)
        & v2_normsp_1(C)
        & l1_normsp_1(C) )
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                 => ( ( r1_nfcont_2(A,C,D,E)
                      & r1_nfcont_2(B,C,D,F) )
                   => r1_nfcont_2(k3_xboole_0(A,B),C,D,k2_vfunct_1(u1_struct_0(C),D,E,F)) ) ) ) ) ) )).

fof(t4_nfcont_2,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_numbers)
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v7_rlvect_1(C)
            & v2_normsp_1(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( ~ v3_struct_0(D)
                & v3_rlvect_1(D)
                & v4_rlvect_1(D)
                & v5_rlvect_1(D)
                & v6_rlvect_1(D)
                & v7_rlvect_1(D)
                & v2_normsp_1(D)
                & l1_normsp_1(D) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
                 => ( r1_nfcont_2(A,C,D,E)
                   => r1_nfcont_2(A,C,D,k4_vfunct_1(u1_struct_0(C),D,E,B)) ) ) ) ) ) )).

fof(t5_nfcont_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v7_rlvect_1(C)
            & v2_normsp_1(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
             => ( r1_nfcont_2(A,B,C,D)
               => r1_nfcont_2(A,B,C,k6_vfunct_1(u1_struct_0(B),C,D)) ) ) ) ) )).

fof(t6_nfcont_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v7_rlvect_1(C)
            & v2_normsp_1(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
             => ( r1_nfcont_2(A,B,C,D)
               => r2_nfcont_2(A,B,k2_nfcont_1(B,C,D)) ) ) ) ) )).

fof(t7_nfcont_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v7_rlvect_1(C)
            & v2_normsp_1(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
             => ( r1_nfcont_2(A,B,C,D)
               => r3_nfcont_1(B,C,D,A) ) ) ) ) )).

fof(t8_nfcont_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,u1_struct_0(B),k1_numbers) )
         => ( r2_nfcont_2(A,B,C)
           => r4_nfcont_1(B,C,A) ) ) ) )).

fof(t9_nfcont_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v7_rlvect_1(C)
            & v2_normsp_1(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
             => ( r5_nfcont_1(B,C,A,D)
               => r1_nfcont_2(A,B,C,D) ) ) ) ) )).

fof(t10_nfcont_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( v1_nfcont_1(D,B)
                      & r3_nfcont_1(B,A,C,D) )
                   => r1_nfcont_2(D,B,A,C) ) ) ) ) ) )).

fof(t11_nfcont_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( r1_tarski(D,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
                      & v1_nfcont_1(D,B)
                      & r1_nfcont_2(D,B,A,C) )
                   => v1_nfcont_1(k10_relset_1(u1_struct_0(B),u1_struct_0(A),C,D),A) ) ) ) ) ) )).

fof(t12_nfcont_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( C != k1_xboole_0
                  & r1_tarski(C,k4_relset_1(u1_struct_0(A),k1_numbers,B))
                  & v1_nfcont_1(C,A)
                  & r2_nfcont_2(C,A,B)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(D,C)
                              & r2_hidden(E,C)
                              & k4_finseq_4(u1_struct_0(A),k1_numbers,B,D) = k4_seq_4(k10_relset_1(u1_struct_0(A),k1_numbers,B,C))
                              & k4_finseq_4(u1_struct_0(A),k1_numbers,B,E) = k5_seq_4(k10_relset_1(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) ) ) )).

fof(t13_nfcont_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v7_rlvect_1(C)
            & v2_normsp_1(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
             => ( ( r1_tarski(A,k4_relset_1(u1_struct_0(B),u1_struct_0(C),D))
                  & r1_partfun2(u1_struct_0(B),u1_struct_0(C),D,A) )
               => r1_nfcont_2(A,B,C,D) ) ) ) ) )).

fof(d3_nfcont_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & v4_lopban_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( m1_nfcont_2(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(C,np__0)
                & ~ r1_xreal_0(np__1,C)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => r1_xreal_0(k1_normsp_1(A,k6_rlvect_1(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E))),k4_real_1(C,k1_normsp_1(A,k6_rlvect_1(A,D,E)))) ) ) ) ) ) ) )).

fof(t14_nfcont_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & v4_lopban_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ~ ( m1_nfcont_2(B,A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = C
                      & ! [D] :
                          ( m1_subset_1(D,u1_struct_0(A))
                         => ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D) = D
                           => C = D ) ) ) ) ) ) ) )).

fof(t15_nfcont_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & v4_lopban_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ~ ( ? [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & m1_nfcont_2(k1_abian(u1_struct_0(A),B,C),A) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = C
                      & ! [D] :
                          ( m1_subset_1(D,u1_struct_0(A))
                         => ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D) = D
                           => C = D ) ) ) ) ) ) ) )).

fof(t16_nfcont_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(A,np__0)
                  & ~ r1_xreal_0(np__1,A)
                  & ~ r1_xreal_0(C,np__0)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => r1_xreal_0(C,k18_complex1(k3_xcmplx_0(B,k3_power(A,D)))) ) ) ) ) ) )).

fof(dt_m1_nfcont_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & v4_lopban_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( m1_nfcont_2(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) ) ) )).

fof(existence_m1_nfcont_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & v4_lopban_1(A)
        & l1_normsp_1(A) )
     => ? [B] : m1_nfcont_2(B,A) ) )).
%------------------------------------------------------------------------------