theorem
  for F being Function st F is Finite_Sep_Sequence of S holds union rng F in S
proof
  let F be Function;
  assume F is Finite_Sep_Sequence of S;
then  ex G being Sep_Sequence of S st union rng F = union rng G
  &( for n st n in dom F holds F.n = G.n)& for m st not m in dom F holds G.m =
  {} by Th30;
  hence thesis;
end;
