reserve n for Element of NAT;

theorem
  for P, Q being non empty Subset of TOP-REAL n st P is compact & Q is
  compact holds HausDist (P, Q) >= 0
proof
  let P, Q be non empty Subset of TOP-REAL n;
A1: the TopStruct of TOP-REAL n = TopSpaceMetr Euclid n by EUCLID:def 8;
  then reconsider P1 = P, Q1 = Q as non empty Subset of TopSpaceMetr Euclid n;
  assume P is compact & Q is compact;
  then P1 is compact & Q1 is compact by A1,COMPTS_1:23;
  then HausDist (P1, Q1) >= 0 by Th35;
  hence thesis by Def3;
end;
