theorem
  seq is convergent & lim seq = g implies ||.(z * seq) - (z * g).|| is
  convergent & lim ||.(z * seq) - (z * g).|| = 0
proof
  assume seq is convergent & lim seq = g;
  then z * seq is convergent & lim (z * seq) = z * g by Th5,Th15;
  hence thesis by Th22;
end;
