theorem Th38:
  for A,B being non empty Subset of TOP-REAL n holds dist_min(A,B) >= 0
proof
  let A,B be non empty Subset of TOP-REAL n;
  ex A9,B9 be Subset of TopSpaceMetr Euclid n st A = A9 & B = B9 &
  dist_min(A,B) = min_dist_min(A9,B9) by Def1;
  hence thesis by Th11;
end;
