reserve n for Element of NAT;

theorem
  for P being non empty Subset of TOP-REAL n holds HausDist (P, P) = 0
proof
  let P be non empty Subset of TOP-REAL n;
  the TopStruct of TOP-REAL n = TopSpaceMetr Euclid n by EUCLID:def 8;
  then reconsider P1 = P as non empty Subset of TopSpaceMetr Euclid n;
  HausDist (P1, P1) = 0 by Th29;
  hence thesis by Def3;
end;
