
theorem NF910:
  for a being non empty positive at_most_one FinSequence of REAL,
  h being non empty FinSequence of NAT*,
  f being FinSequence of NAT st
  f = OnlinePacking(a, NextFit(a)) holds
  ex k being Nat st rng f = Seg k
  proof
    let a be non empty positive at_most_one FinSequence of REAL,
    h be non empty FinSequence of NAT*, f be FinSequence of NAT;

    assume HL00: f = OnlinePacking(a, NextFit(a));

    set h = OnlinePackingHistory(a, NextFit(a)), i = len h;

    L200: 1 <= i by NAT_1:14;

    L220: i <= len a by defPackHistory;

    ex k being Nat st rng (h . i) = Seg k & (h . i) . i = k by L200,L220,NF805;
    hence ex k being Nat st rng f = Seg k by HL00;
  end;
