Proof using lmi smsi misi si.
red. unfold client_cache_correct in *. simpl in *. intros. subst.
find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
use_same_client_cache handleAppendEntries_clientCache.
erewrite handleAppendEntries_preserves_lastApplied_entries; eauto.
Qed.

Lemma client_cache_correct_append_entries_reply :
raft_net_invariant_append_entries_reply' client_cache_correct.