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 Th11
    .= ((lim s) * (lim s9))*' by Th20
    .= (lim s)*' * (lim s9)*' by COMPLEX1:35;
end;
