
theorem NF540:
  for a being non empty FinSequence of REAL,
  Alg being Function of [:REAL, NAT*:],NAT,
  h being non empty FinSequence of NAT*,
  f being non empty FinSequence of NAT holds
  dom OnlinePacking(a, Alg) = dom a
  proof
    let a be non empty FinSequence of REAL,
    Alg be Function of [:REAL, NAT*:],NAT,
    h be non empty FinSequence of NAT*, f be non empty FinSequence of NAT;

    set f = OnlinePacking(a, Alg), h = OnlinePackingHistory(a, Alg);

    L220: len h = len a by defPackHistory;

    1 <= len h by NAT_1:14;
    then len (h . (len h)) = len h by L220,NF510;
    hence dom f = dom a by L220,FINSEQ_3:29;
  end;
