theorem
  x0 in dom f & f is_continuous_in x0 implies
    |. f .| is_continuous_in x0
  proof
    assume
A1: x0 in dom f & f is_continuous_in x0;
    reconsider g = f as PartFunc of REAL,REAL-NS n
      by REAL_NS1:def 4;
    g is_continuous_in x0 by A1;
    then ||. g .|| is_continuous_in x0 by NFCONT_3:14;
    hence thesis by Th9;
  end;
