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 Th20:
  n <> 0 & e1 in OpenHypercube(e,r) implies r > abs(e1-e).max_diff_index(e1,e)
  proof
    set d = max_diff_index(e1,e);
    abs(e1-e).d = |.(e1-e).d.| by VALUED_1:18;
    hence thesis by Th14;
  end;
