Proof using.
unfold refined_raft_net_invariant_append_entries, leaderLogs_sublog.
simpl. intuition.
repeat find_higher_order_rewrite.
find_copy_apply_lem_hyp handleAppendEntries_type.
intuition.
- start.
find_rewrite_lem update_elections_data_appendEntries_leaderLogs.
find_erewrite_lem update_nop_ext'.
update_destruct_max_simplify; eauto.
erewrite handleAppendEntries_leader by (eauto; congruence).
eauto.
- repeat update_destruct_max_simplify; try congruence.
+ find_rewrite_lem update_elections_data_appendEntries_leaderLogs.
eauto.
+ eauto.
Qed.

Theorem leaderLogs_sublog_append_entries_reply :
refined_raft_net_invariant_append_entries_reply leaderLogs_sublog.