
theorem
  for S being Scott complete TopLattice, T being complete LATTICE, A
being Scott TopAugmentation of T st the RelStr of S = the RelStr of T holds the
  TopRelStr of A = the TopRelStr of S
proof
  let S be Scott complete TopLattice, T be complete LATTICE, A be Scott
  TopAugmentation of T such that
A1: the RelStr of S = the RelStr of T;
A2: the topology of S = sigma S by WAYBEL14:23
    .= sigma T by A1,YELLOW_9:52
    .= the topology of A by YELLOW_9:51;
  the RelStr of A = the RelStr of S by A1,YELLOW_9:def 4;
  hence thesis by A2;
end;
