Proof using.
red. unfold client_cache_correct in *. simpl in *. intros. subst.
find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
use_same_client_cache handleTimeout_clientCache.
erewrite handleTimeout_lastApplied; eauto.
erewrite handleTimeout_log_same; eauto.
Qed.

Lemma client_cache_correct_do_leader :
raft_net_invariant_do_leader' client_cache_correct.