simple induction l. auto with arith.
intros. simpl in |- *. rewrite H. trivial with arith.
Qed.
(****************************************************************)
(* Decidabilite *)

(* Specifications: *)
Lemma eq_cons :
forall (l1 l2 : list A) (a1 a2 : A), a1 :: l1 = a2 :: l2 -> l1 = l2.