inversion H.
apply FreeCons.
+ apply FreeCons.
- constructor.
- intros. inversion H4.
+ intros.
subst.
eapply H3.
- instantiate (1 := l2); left; auto.
- inversion H4.
* subst. inversion H4. subst. instantiate (1:= p1); instantiate (1 := p2).
auto.
* inversion H0.
- inversion H0.
Qed.

(* Specifications: *)
Lemma PosToPathPrefixFree : forall (x y : positive), (x <> y) ->
PrefixFree [posToPath x;
posToPath y].