theorem
  seq is convergent & lim seq = g implies ||.z * seq.|| is convergent &
  lim ||.z * seq.|| = ||.z * g.||
proof
  assume seq is convergent & lim seq = g;
  then z * seq is convergent & lim (z * seq) = z * g by Th5,Th15;
  hence thesis by Th21;
end;
