
theorem Th2:
  for L1,L2 being TopSpace-like lower non empty TopRelStr st the
  RelStr of L1 = the RelStr of L2 holds the topology of L1 = the topology of L2
proof
  let L1,L2 be TopSpace-like lower non empty TopRelStr such that
A1: the RelStr of L1 = the RelStr of L2;
  set B2 = the set of all (uparrow x)` where x is Element of L2;
  set B1 = the set of all (uparrow x)` where x is Element of L1;
A2: B1 is prebasis of L1 by Def1;
A3: B2 is prebasis of L2 by Def1;
  B1 = B2 by A1,Lm1;
  hence thesis by A1,A2,A3,YELLOW_9:26;
end;
