Proof using.
red. unfold append_entries_leaderLogs. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- prove_in. eapply_prop_hyp In In; break_exists. intuition; eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
rewrite update_elections_data_appendEntries_leaderLogs; eauto;
subst; auto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
rewrite update_elections_data_appendEntries_leaderLogs; eauto;
subst; auto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
rewrite update_elections_data_appendEntries_leaderLogs; eauto;
subst; auto.
+ eauto.
- subst. simpl in *.
unfold handleAppendEntries in *.
repeat break_match; find_inversion; congruence.
Qed.

(* Specifications: *)
Lemma append_entries_leaderLogs_appendEntriesReply :
refined_raft_net_invariant_append_entries_reply append_entries_leaderLogs.