elim non_vide_V; intros u H1; clear H1.
elim angle_cons with (a := a) (u := u); intros v H1; try exact H1.
apply transitive with (plus zero (cons u v)).
apply compatible.
apply reflexive.
try exact H1.
apply transitive with (cons u v).
apply zero_plus.
apply symetrique; auto.
Qed.

(* Specifications: *)
Lemma R_permute :
forall u v w t : V, R (cons u v) (cons w t) -> R (cons v u) (cons t w).