Proof using.
unfold msg_refined_raft_net_invariant_append_entries_reply,
lifted_maxIndex_sanity, maxIndex_lastApplied, maxIndex_commitIndex.
intuition; repeat find_higher_order_rewrite; update_destruct_simplify; auto.
- erewrite handleAppendEntriesReply_same_lastApplied by eauto.
erewrite handleAppendEntriesReply_same_log by eauto.
auto.
- erewrite handleAppendEntriesReply_same_commitIndex by eauto.
erewrite handleAppendEntriesReply_same_log by eauto.
auto.
Qed.

(* Specifications: *)
Lemma lifted_maxIndex_sanity_request_vote :
msg_refined_raft_net_invariant_request_vote lifted_maxIndex_sanity.