
theorem Th38:
  for M being non empty MetrSpace, P, Q, R being non empty Subset
of TopSpaceMetr M st P is compact & Q is compact & R is compact holds HausDist
  (P, R) <= HausDist (P, Q) + HausDist (Q, R)
proof
  let M be non empty MetrSpace, P, Q, R be non empty Subset of TopSpaceMetr M;
  assume P is compact & Q is compact & R is compact;
  then
  max_dist_min (P, R) <= HausDist (P, Q) + HausDist (Q, R) & max_dist_min
  (R, P) <= HausDist (P, Q) + HausDist (Q, R) by Th33;
  hence thesis by XXREAL_0:28;
end;
