Proof using.
red. unfold log_properties_hold_on_leader_logs. intros.
simpl in *.
subst. repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto; [|finish].
find_erewrite_lem update_elections_data_appendEntries_leaderLogs; eauto.
finish.
Qed.

Lemma log_properties_hold_on_leader_logs_append_entries_reply :
refined_raft_net_invariant_append_entries_reply log_properties_hold_on_leader_logs.