apply transitive with (cons (vec A B) (opp (vec A B))); auto.
apply vR_R_compatible; auto.
apply v_sym; apply opp_vect.
Qed.
Hint Resolve abba.

Lemma calcul5 :
forall a b c d : AV,
R (plus (plus a (plus b c)) (plus d d))
(plus a (plus (plus d b) (plus d c))).