
theorem Th3:
  for R1,R2 being non empty RelStr st the RelStr of R1 = the RelStr
  of R2 holds omega R1 = omega R2
proof
  let R1,R2 be non empty RelStr such that
A1: the RelStr of R1 = the RelStr of R2;
  set S = the lower correct TopAugmentation of R1;
  the RelStr of S = the RelStr of R1 by YELLOW_9:def 4;
  then
A2: S is TopAugmentation of R2 by A1,YELLOW_9:def 4;
  omega R1 = the topology of S by Def2;
  hence thesis by A2,Def2;
end;
