 reserve n for Nat;
 reserve s1 for sequence of Euclid n,
         s2 for sequence of REAL-NS n;

theorem
  for r being Real holds vol {r} = 0
  proof
    let r be Real;
    vol {r} = upper_bound {r} - lower_bound {r} by INTEGRA1:def 5
           .= r - lower_bound {r} by SEQ_4:9
           .= r - r by SEQ_4:9;
    hence thesis;
  end;
