theorem
  for n being Nat holds Seg n -->
    the_set_of_all_closed_real_bounded_intervals is n-element FinSequence
  proof
    let n be Nat;
    reconsider f = Seg n --> the_set_of_all_closed_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;
