reserve X for set,
  Y for non empty set;
reserve n for Nat;
reserve r for Real,
  M for non empty MetrSpace;
reserve n for Nat,
  p,q,q1,q2 for Point of TOP-REAL 2,
  r,s1,s2,t1,t2 for Real,
  x,y for Point of Euclid 2;

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;
