reserve a, b, c, d, r, s for Real,
  n for Element of NAT,
  p, p1, p2 for Point of TOP-REAL 2,
  x, y for Point of TOP-REAL n,
  C for Simple_closed_curve,
  A, B, P for Subset of TOP-REAL 2,
  U, V for Subset of (TOP-REAL 2)|C`,
  D for compact with_the_max_arc Subset of TOP-REAL 2;

theorem Th16:
  for n being Nat
  for r being positive Real
  for a being Point of TOP-REAL n holds a in Ball(a,r)
proof let n be Nat;
  let r be positive Real;
  let a be Point of TOP-REAL n;
  |. a-a .| = 0 by TOPRNS_1:28;
  hence thesis by TOPREAL9:7;
end;
