Proof using.
induction l; simpl in *; intros.
- find_inversion. auto.
- repeat break_match; find_inversion; simpl in *;
unfold cacheApplyEntry, applyEntry in *;
repeat break_match; find_inversion; simpl in *; eauto;
copy_eapply_prop_hyp applyEntries applyEntries; intuition; simpl in *; auto.
Qed.

Lemma filter_false :
forall A (l : list A),
filter (fun _ => false) l = [].