
theorem
  for S,T being complete LATTICE st the RelStr of S = the RelStr of T
  holds sigma S = sigma T
proof
  let S,T be complete LATTICE such that
A1: the RelStr of S = the RelStr of T;
  set A = the Scott correct TopAugmentation of S;
  the RelStr of A = the RelStr of S by Def4;
  then A is Scott correct TopAugmentation of T by A1,Def4;
  then the topology of A = sigma T by Th51;
  hence thesis by Th51;
end;
