Proof using.
unfold cacheApplyEntry.
intros.
repeat break_match_hyp; repeat find_inversion; do_bool; intuition eauto with *;
right; (split; [solve [apply applyEntry_clientCache; auto]|]); auto.
right. do_bool. eexists. eexists. intuition eauto. omega.
Qed.

Lemma getLastId_ext :
forall st st' c,
clientCache st' = clientCache st ->
getLastId st' c = getLastId st c.