theorem
  seq is convergent & lim seq = g implies dist((a * seq) , (a * g)) is
  convergent & lim dist((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 Th24;
end;
