
theorem

:: 1.3. LEMMA, p. 143 (variant II)
  for S,T being lower lower-bounded non empty TopPoset holds omega [:S
  ,T qua Poset:] = the topology of [:S,T qua non empty TopSpace:]
proof
  let S,T be lower lower-bounded non empty TopPoset;
A1: T is TopAugmentation of T by YELLOW_9:44;
  S is TopAugmentation of S by YELLOW_9:44;
  hence thesis by A1,Th15;
end;
