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_2:26;
end;
