Proof using.
red. intros. unfold in_any_log_term_was_created. intros.
unfold in_any_log_term_was_created, term_was_created in *.
iae_case.
- repeat find_reverse_higher_order_rewrite.
find_eapply_lem_hyp in_log.
eapply_prop_hyp in_any_log in_any_log.
break_exists_exists; repeat find_higher_order_rewrite; eauto.
- find_apply_hyp_hyp.
find_eapply_lem_hyp in_aer; eauto.
eapply_prop_hyp in_any_log in_any_log.
break_exists_exists; repeat find_higher_order_rewrite; eauto.
- repeat find_reverse_higher_order_rewrite.
find_eapply_lem_hyp in_ll; eauto.
eapply_prop_hyp in_any_log in_any_log.
break_exists_exists; repeat find_higher_order_rewrite; eauto.
Qed.

Lemma in_any_log_term_was_created_reboot :
refined_raft_net_invariant_reboot in_any_log_term_was_created.