Proof using lmi smsi misi si.
red. unfold state_machine_log in *. simpl in *. intros.
find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
erewrite handleAppendEntries_stateMachine; eauto.
erewrite handleAppendEntries_preserves_lastApplied_entries; eauto.
Qed.

Lemma state_machine_append_entries_reply :
raft_net_invariant_append_entries_reply' state_machine_log.