
theorem :: THEOREM 4.7 (6)
  for L1 be continuous lower-bounded sup-Semilattice st L1 is infinite
  holds CLweight L1 = CLweight InclPoset sigma L1
proof
  let L1 be continuous lower-bounded sup-Semilattice;
  set S = the Scott TopAugmentation of L1;
  assume
A1: L1 is infinite;
A2: CLweight L1 = weight S & InclPoset the topology of S = InclPoset sigma
  L1 by Th24,YELLOW_9:51;
  the RelStr of S = the RelStr of L1 by YELLOW_9:def 4;
  then S is infinite by A1;
  hence thesis by A2,Th6;
end;
