reserve n   for Nat,
        r,s for Real,
        x,y for Element of REAL n,
        p,q for Point of TOP-REAL n,
        e   for Point of Euclid n;
reserve n for non zero Nat;
reserve n for non zero Nat;
reserve n for Nat,
        X for set,
        S for Subset-Family of X;

theorem
  for n being Nat holds Seg n --> the_set_of_all_open_real_bounded_intervals is
    n-element FinSequence
  proof
    let n be Nat;
    reconsider f = Seg n --> the_set_of_all_open_real_bounded_intervals as
      FinSequence;
    dom f is n-element by FUNCOP_1:13;
    then card dom f = n by CARD_1:def 7;
    then card f = n by CARD_1:62;
    hence thesis by CARD_1:def 7;
  end;
