
theorem Th2:
  for T being discrete non empty TopSpace holds T is normal
proof
  let T be discrete non empty TopSpace;
  let W, V be Subset of T such that
  W <> {} and
  V <> {} and
  W is closed and
  V is closed and
A1: W /\ V = {};
  take P = W, Q = V;
  thus P is open & Q is open by TDLAT_3:15;
  thus W c= P & V c= Q & P /\ Q = {} by A1;
end;
