+ simpl in H. inversion H.
+ inversion H.
- split.
* subst. unfold lt. apply le_n.
* congruence.
- apply IHn in H0; inversion H0; clear H0; split.
* unfold lt in *.
apply le_S.
auto.
* auto.
Qed.

(* Specifications: *)
Lemma rangePosPrefixFree : forall p, PrefixFree (map posToPath (rangePos p)).
intros.