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 being convergent Complex_Sequence
   holds lim |.(r(#)s).| = |.r.|*|.(lim s).|
proof
  let s being convergent Complex_Sequence;
  thus lim |.(r(#)s).| = |.lim (r(#)s).| by Th27
    .= |.r*(lim s).| by COMSEQ_2:18
    .= |.r.|*|.(lim s).| by COMPLEX1:65;
end;
