
theorem Th33:
  for R being complete LATTICE holds lambda R = UniCl FinMeetCl ((
  sigma R) \/ (omega R))
proof
  let R be complete LATTICE;
  set S = the Lawson correct TopAugmentation of R;
A1: the RelStr of S = the RelStr of R by YELLOW_9:def 4;
  then
A2: sigma R = sigma S by YELLOW_9:52;
  (omega S) \/ sigma S is prebasis of S by Def3;
  then FinMeetCl ((omega S) \/ sigma S) is Basis of S by YELLOW_9:23;
  then
A3: the topology of S = UniCl FinMeetCl ((omega S) \/ sigma S) by YELLOW_9:22;
  omega R = omega S by A1,Th3;
  hence thesis by A3,A1,A2,Def4;
end;
