
theorem Th24: :: THEOREM 4.7 (1)=(2)
  for L1 be continuous lower-bounded sup-Semilattice for T be
  Scott TopAugmentation of L1 holds CLweight L1 = weight T
proof
  let L1 be continuous lower-bounded sup-Semilattice;
  let T be Scott TopAugmentation of L1;
  set T1 = the Lawson correct TopAugmentation of L1;
  weight T c= weight T1 & weight T1 c= CLweight L1 by Lm1,Lm2;
  then
A1: weight T c= CLweight L1;
  CLweight L1 c= weight T by Lm3;
  hence thesis by A1,XBOOLE_0:def 10;
end;
