reserve X for non empty TopSpace;
reserve Y for non empty TopStruct;
reserve x for Point of Y;
reserve Y for non empty TopStruct;

theorem Th15:
  for A being empty Subset of Y holds A is not maximal_anti-discrete
proof
  consider a being object such that
A1: a in the carrier of Y by XBOOLE_0:def 1;
  reconsider a as Point of Y by A1;
  let A be empty Subset of Y;
  now
    take C = {a};
    thus C is anti-discrete & A c= C & A <> C by Th6;
  end;
  hence thesis;
end;
