reserve n,n1,n2,m for Nat,
  r,r1,r2,p,g1,g2,g for Real,
  seq,seq9,seq1 for Real_Sequence,
  y for set;
reserve g for Complex;
reserve s,s1,s9 for Complex_Sequence;

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;
