theorem
  seq9 is convergent & seq is convergent & lim seq <> 0
  & seq is non-zero implies seq9/"seq is convergent
proof
  assume that
A1: seq9 is convergent and
A2: seq is convergent and
A3: (lim seq)<>0 and
A4: seq is non-zero;
  seq" is convergent by A2,A3,A4,Th21;
  hence thesis by A1;
end;
