Proof using.
red. unfold state_machine_log in *. simpl in *. intros. subst.
find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
erewrite doLeader_stateMachine; eauto.
erewrite doLeader_same_log; eauto.
erewrite doLeader_lastApplied; eauto.
Qed.

Lemma state_machine_reboot :
raft_net_invariant_reboot' state_machine_log.