theorem
  s9 is convergent & s is convergent & (lim s)<>0c & s is non-zero
  implies lim |.(s9/"s).|=|.(lim s9).|/|.(lim s).|
proof
  assume
A1: s9 is convergent & s is convergent & (lim s)<>0c & s is non-zero;
  then s9/"s is convergent by COMSEQ_2:38;
  hence lim |.s9/"s.| = |.lim (s9/"s).| by Th27
    .= |.(lim s9)/(lim s).| by A1,COMSEQ_2:39
    .= |.(lim s9).|/|.(lim s).| by COMPLEX1:67;
end;
