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
  for C being non empty Subset of TOP-REAL n for D being Subset of
TOP-REAL n st C c= D for q being Point of TOP-REAL n holds dist(q,D) <= dist(q,
  C) by Th41;
