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