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;
