Proof using.
induction es; intros; simpl in *.
- find_inversion. auto.
- repeat break_match; find_inversion;
find_apply_hyp_hyp;
find_apply_lem_hyp cacheApplyEntry_spec;
intuition; repeat find_rewrite; auto.
Qed.

(* Specifications: *)
Lemma output_correct_prefix :
forall l1 l2 client id out,
Prefix l1 l2 ->
output_correct client id out l1 ->
output_correct client id out l2.