Proof using.
red. unfold lastApplied_le_commitIndex. intros.
simpl in *. repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
find_copy_apply_lem_hyp handleAppendEntriesReply_same_lastApplied.
repeat find_rewrite.
find_copy_apply_lem_hyp handleAppendEntriesReply_same_commitIndex.
repeat find_rewrite. eauto.
Qed.

Lemma lastApplied_le_commitIndex_requestVote :
raft_net_invariant_request_vote lastApplied_le_commitIndex.