Proof using.
red. unfold lastApplied_le_commitIndex. intros.
subst.
simpl in *. repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
find_copy_apply_lem_hyp handleTimeout_commitIndex.
find_copy_apply_lem_hyp handleTimeout_lastApplied.
repeat find_rewrite. eauto.
Qed.

(* Specifications: *)
Lemma lastApplied_le_commitIndex_reboot :
raft_net_invariant_reboot lastApplied_le_commitIndex.