Proof using.
unfold msg_refined_raft_net_invariant_request_vote_reply,
lifted_maxIndex_sanity, maxIndex_lastApplied, maxIndex_commitIndex.
intuition; repeat find_higher_order_rewrite; update_destruct_simplify; auto.
- rewrite handleRequestVoteReply_same_log.
rewrite handleRequestVoteReply_same_lastApplied.
auto.
- rewrite handleRequestVoteReply_same_log.
rewrite handleRequestVoteReply_same_commitIndex.
auto.
Qed.

Lemma doLeader_same_lastApplied :
forall st n os st' ms,
doLeader st n = (os, st', ms) ->
lastApplied st' = lastApplied st.