intros u H; try assumption.
apply transitive with (plus (cons u (opp u)) (cons (opp u) u)).
apply compatible.
apply symetrique; auto.
apply angle_plat.
apply symetrique; auto.
apply oppu_u.
apply transitive with (cons u u).
apply Chasles.
auto.
apply angle_nul.
Qed.

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