inversion Corr as [Vary_In In_Vary Pref]; clear Corr.
destruct l as [ | p ps]; auto.
clear Vary_In Pref.
pose proof (In_Vary p) as Contra; clear In_Vary.
fireInLeft Hyp.
inversion Hyp.
Qed.

(* Specifications: *)
Lemma PrefixFreeWithNil : forall l, PrefixFree ([] :: l) -> l = [].
intros.