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

theorem Th38:
  for s being non empty increasing FinSequence of REAL,
      r being Real st s.len s < r holds
    s ^ <*r*> is non empty increasing FinSequence of REAL
  proof
    let s be non empty increasing FinSequence of REAL,
    r be Real;
    assume s.len s < r;
    then s.len s < <*r*>.1;
    hence thesis by Th1;
  end;
