
theorem

:: 1.6. PROPOSITION (i), p. 144
  for S being Scott complete TopLattice for T being Lawson correct
  TopAugmentation of S for A being upper Subset of T st A is open for C being
  Subset of S st C = A holds C is open
proof
  let S be Scott complete TopLattice;
  let T be Lawson correct TopAugmentation of S;
  let A be upper Subset of T;
  assume
A1: A is open;
  let C be Subset of S;
A2: the RelStr of T = the RelStr of S by YELLOW_9:def 4;
  assume C = A;
  then C is upper property(S) by A1,Th36,A2,WAYBEL_0:25,YELLOW12:19;
  hence thesis by WAYBEL11:15;
end;
