Proof using.
intros.
unfold cacheApplyEntry, applyEntry in *.
repeat break_match; subst; repeat find_inversion; do_bool;
simpl in *; auto; try omega; congruence.
Qed.

Lemma clientCache_to_ks_assoc_set :
forall c client id o,
assoc_set clientId_eq_dec (clientCache_to_ks c) client id =
clientCache_to_ks (assoc_set clientId_eq_dec c client (id, o)).