Proof using.
red. unfold leaderLogs_votesWithLog. intros. simpl in *.
subst. repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
- find_rewrite_lem update_elections_data_appendEntries_leaderLogs.
eapply quorum_preserved; [|eauto].
intros.
find_higher_order_rewrite; destruct_update; simpl in *; eauto.
rewrite votesWithLog_same_append_entries. auto.
- eapply quorum_preserved; [|eauto].
intros.
find_higher_order_rewrite; destruct_update; simpl in *; eauto.
rewrite votesWithLog_same_append_entries. auto.
Qed.

Lemma leaderLogs_votesWithLog_append_entries_reply :
refined_raft_net_invariant_append_entries_reply leaderLogs_votesWithLog.