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