theorem
  for p be Element of S, r be Real st 0 < r
  holds Ball(p,r) is Neighbourhood of p
  proof
    let p be Element of S,r be Real;
    assume 0 < r; then
    {y where y is Point of S: ||.y - p.|| < r}
        is Neighbourhood of p by NFCONT_1:3;
    hence thesis by LMBALL;
  end;
