intros u v w t; try assumption.
apply transitive with (plus (cons u v) (cons v t)).
apply symetrique; auto.
apply Chasles.
apply compatible.
apply reflexive.
apply symetrique; auto.
apply Chasles.
Qed.

Lemma plus_assoc :
forall a b c : AV, R (plus a (plus b c)) (plus (plus a b) c).