Proof using.
red. unfold terms_and_indices_from_one_log_ind. split; red; simpl in *; intuition.
- find_higher_order_rewrite. update_destruct; subst; rewrite_update; auto.
find_apply_lem_hyp handleTimeout_log_same. find_rewrite. auto.
- eapply taifol_no_append_entries; eauto using handleTimeout_packets.
Qed.

Lemma terms_and_indices_from_one_app :
forall xs ys,
terms_and_indices_from_one xs ->
terms_and_indices_from_one ys ->
terms_and_indices_from_one (xs ++ ys).