apply transitive with (plus (cons u v) (cons v (opp v))).
apply symetrique; auto.
apply Chasles.
apply compatible.
apply reflexive.
apply angle_plat.
Qed.

(* Specifications: *)
Lemma oppu_v : forall u v : V, R (cons (opp u) v) (plus pi (cons u v)).
intros u v; try assumption.