Proof using.
unfold refined_raft_net_invariant_timeout, allEntries_leaderLogs_term.
simpl. intros.
repeat find_higher_order_rewrite.
destruct_update.
- simpl in *.
find_rewrite_lem update_elections_data_timeout_allEntries.
find_apply_hyp_hyp.
intuition.
right. break_exists_exists.
find_higher_order_rewrite.
destruct_update.
+ simpl in *. rewrite update_elections_data_timeout_leaderLogs. intuition.
+ intuition.
- find_apply_hyp_hyp.
intuition.
right.
break_exists_exists.
find_higher_order_rewrite.
destruct_update.
+ simpl in *. rewrite update_elections_data_timeout_leaderLogs. intuition.
+ intuition.
Qed.

Lemma allEntries_leaderLogs_term_append_entries_reply :
refined_raft_net_invariant_append_entries_reply allEntries_leaderLogs_term.