
theorem :: THEOREM 4.7 (1)=(3)
  for L1 be continuous lower-bounded sup-Semilattice for T be Lawson
  correct TopAugmentation of L1 holds CLweight L1 = weight T
proof
  let L1 be continuous lower-bounded sup-Semilattice;
  let T be Lawson correct TopAugmentation of L1;
  set T1 = the Scott TopAugmentation of L1;
  CLweight L1 c= weight T1 & weight T1 c= weight T by Lm1,Lm3;
  then
A1: CLweight L1 c= weight T;
  weight T c= CLweight L1 by Lm2;
  hence thesis by A1,XBOOLE_0:def 10;
end;
