(** * Exercice 4 *)
(* 10:36 *)

Fixpoint u (n : nat) : R :=
  match n with
    | O => 2
    | S n => 2/3 * u n + 1/3 * (INR n) + 1
  end.

(* Specifications: *)
Lemma Q2a : forall n, u n <= INR n + 3.
Lemma Q2b : forall n, u (S n) - u n = 1/3 * (INR n + 3 - u n).
Lemma Q2c : forall n, u n <= u (S n).