Proof using.
red. intros. unfold in_any_log_term_was_created. intros.
eapply term_was_created_preserved; [eapply_prop in_any_log_term_was_created|];
[|intros; simpl in *;
repeat find_higher_order_rewrite;
destruct_update; simpl in *; eauto;
rewrite update_elections_data_timeout_leaderLogs; eauto].
iae_case.
- repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
find_eapply_lem_hyp handleTimeout_log_same; eauto.
repeat find_rewrite. eauto.
- find_apply_hyp_hyp. intuition; eauto.
do_in_map. subst. simpl in *.
find_eapply_lem_hyp handleTimeout_not_is_append_entries; eauto.
intuition. find_false.
unfold mEntries in *. break_match; try congruence.
repeat eexists; eauto.
- repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
find_rewrite_lem update_elections_data_timeout_leaderLogs; eauto.
Qed.

Lemma in_any_log_term_was_created_do_leader :
refined_raft_net_invariant_do_leader in_any_log_term_was_created.