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

theorem
  for I being non empty closed_interval Subset of REAL,
  D being Division of I, T being Element of set_of_tagged_Division(D) holds
  rng T c= REAL
  proof
    let I be non empty closed_interval Subset of REAL,
    D be Division of I, T be Element of set_of_tagged_Division(D);
    ex s be non empty non-decreasing FinSequence of REAL st
    T = s & dom s = dom D &
    for i be Nat st i in dom s holds s.i in divset(D,i) by Def2;
    hence thesis by FINSEQ_1:def 4;
  end;
