
theorem Th14:
  for s be non empty increasing FinSequence of REAL,
      a be Real
  st s.(len s) < a
  holds s^<*a*> is non empty increasing FinSequence of REAL
  proof
    let s be non empty increasing FinSequence of REAL,
        a be Real;
    assume
    A1: s.(len s) < a;
    reconsider a0 = a as Element of REAL by XREAL_0:def 1;
    reconsider t = <*a0*> as non empty increasing FinSequence of REAL;
    s.(len s) < t.1 by A1;
    hence thesis by Th13;
  end;
