intros u H; try assumption.
apply transitive with (plus (cons u (opp u)) zero).
apply compatible.
apply symetrique.
apply angle_plat.
apply reflexive.
apply transitive with (cons u (opp u)).
apply plus_zero.
apply angle_plat.
Qed.

Lemma zero_plus_a : forall a : AV, R (plus zero a) a.
intros a; try assumption.