Definition Un (n:nat) : Ensemble (point_set X) :=
  match n with
  | O => U0
  | S O => U1
  | S (S _) => Full_set
  end.

(* Specifications: *)
Lemma Un_open: forall n:nat, open (Un n).
Lemma Un_incr: forall n:nat, Included (closure (Un n)) (Un (S n)).