intros u v u' v' H; try assumption.
apply transitive with (plus (cons u u') (plus (cons u' v') (cons v' v))).
apply Chasles_2.
apply symetrique; auto.
apply transitive with (plus (cons u' v') (plus (cons u u') (cons v' v))).
apply transitive with (plus (cons u' v') zero).
apply symetrique.
apply plus_zero.
apply compatible.
apply reflexive.
apply symetrique; auto.
apply transitive with (plus (cons v v') (cons v' v)).
apply compatible.
try exact H.
apply reflexive.
apply transitive with (cons v v).
apply Chasles.
apply angle_nul.
apply calcul.
Qed.

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