
theorem Th35:
  for M being non empty MetrSpace, P, Q being non empty Subset of
  TopSpaceMetr M st P is compact & Q is compact holds HausDist (P, Q) >= 0
proof
  let M be non empty MetrSpace, P, Q be non empty Subset of TopSpaceMetr M;
  assume
A1: P is compact & Q is compact;
  per cases by XXREAL_0:16;
  suppose
    HausDist (P, Q) = max_dist_min (P, Q);
    hence thesis by A1,Th28;
  end;
  suppose
    HausDist (P, Q) = max_dist_min (Q, P);
    hence thesis by A1,Th28;
  end;
end;
