
theorem Th28:
  for M being non empty MetrSpace, P, Q being non empty Subset of
  TopSpaceMetr M st P is compact & Q is compact holds max_dist_min (P, Q) >= 0
proof
  let M be non empty MetrSpace, P, Q be non empty Subset of TopSpaceMetr M;
  assume P is compact & Q is compact;
  then ex x1, x2 being Point of M st x1 in P & x2 in Q & dist( x1,x2) =
  max_dist_min(P,Q) by WEIERSTR:32;
  hence thesis by METRIC_1:5;
end;
