theorem
  for s,s9 being convergent Complex_Sequence
  holds lim |.s(#)s9.| = |.lim s.|*|.lim s9.|
proof
  let s,s9 be convergent Complex_Sequence;
  thus lim |.s(#)s9.| = |.lim (s(#)s9).| by Th27
    .= |.(lim s)*(lim s9).| by COMSEQ_2:30
    .= |.lim s.|*|.lim s9.| by COMPLEX1:65;
end;
