proposition: Lemma adjacent_to_symmetric : Symmetric adjacent_to.
proof: Proof. unfold Symmetric. intros x y H_r. inversion H_r; subst. apply fin_complete_neq. intro H_eq. rewrite H_eq in H. auto. Qed.
imports: Verdi(Verdi) StructTact(Fin) Coq(OrderedType) Coq(MSetInterface)