Proof using.
start.
find_apply_lem_hyp handleAppendEntries_type. intuition; try congruence.
rewrite update_elections_data_appendEntries_leaderLogs.
repeat find_rewrite. eauto.
Qed.

Lemma leaders_have_leaderLogs_appendEntriesReply :
refined_raft_net_invariant_append_entries_reply leaders_have_leaderLogs.