theorem
  Ball(p,r) = OpenHyperInterval(@p - (n|-> r), @p + (n|-> r))
  proof
    reconsider e = p as Point of Euclid n;
    ex a being Element of REAL n st a = e &
      OpenHypercube(e,r) = OpenHyperInterval(a - (n|-> r),
                             a + (n|-> r)) by Th51;
    hence thesis by Th68;
  end;
