apply
transitive with (plus (cons (opp u) u) (plus (cons u v) (cons v (opp v)))).
apply Chasles_2.
apply symetrique; auto.
apply
transitive with (plus (cons u v) (plus (cons (opp u) u) (cons v (opp v)))).
cut (R (plus (cons (opp u) u) (cons v (opp v))) zero).
intros H; try assumption.
apply transitive with (plus (cons u v) zero).
apply symetrique.
apply plus_zero.
apply compatible.
apply reflexive.
apply symetrique; auto.
apply transitive with (plus pi pi).
apply compatible.
apply oppu_u.
apply angle_plat.
apply pi_plus_pi.
apply calcul.
Qed.

Lemma rotation :
forall u v u' v' : V, R (cons u u') (cons v v') -> R (cons u v) (cons u' v').