
theorem Th12:
  for s be non empty increasing FinSequence of REAL,
      m be Nat
  st m in dom s
  holds s|m is non empty increasing FinSequence of REAL
  proof
    let s be non empty increasing FinSequence of REAL,
        m be Nat;
    assume a0: m in dom s; then
    1 <= m <= len s by FINSEQ_3:25; then
    len(s|m) = m by FINSEQ_1:59;
    hence thesis by a0,FINSEQ_3:25;
  end;
