reserve
  x, y for object,
  i, n for Nat,
  r, s for Real,
  f1, f2 for n-element real-valued FinSequence;
reserve e, e1 for Point of Euclid n;

theorem Th17:
  n <> 0 implies OpenHypercube(e,r/sqrt(n)) c= Ball(e,r)
  proof
    assume
A1: n <> 0;
    let x be object;
    assume
A2: x in OpenHypercube(e,r/sqrt(n));
    then reconsider x as Point of Euclid n;
A3: dist(x,e) < r/sqrt(n)*sqrt(n) by A1,A2,Th16;
    r/sqrt(n)*sqrt(n) = r by A1,XCMPLX_1:87;
    hence thesis by A3,METRIC_1:11;
  end;
