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
  s is convergent & (lim s)<>0c & s is non-zero implies lim |.s".| = (|.
  lim s.|)"
proof
  assume
A1: s is convergent & (lim s)<>0c & s is non-zero;
  then s" is convergent by COMSEQ_2:34;
  hence lim |.s".| = |.lim s".| by Th27
    .= |.(lim s)".| by A1,COMSEQ_2:35
    .= (|.lim s.|)" by COMPLEX1:66;
end;
