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].
iae_case.
- repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
find_apply_lem_hyp handleAppendEntriesReply_log.
repeat find_rewrite. eauto.
- find_eapply_lem_hyp handleAppendEntriesReply_packets.
find_apply_hyp_hyp. intuition.
+ match goal with
| _ : In ?p' (_ ++ _) |- _ => eapply in_aer with (p1 := p'); eauto
end.
+ subst. simpl in *. intuition.
- repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
Qed.

Lemma in_any_log_term_was_created_request_vote_reply :
refined_raft_net_invariant_request_vote_reply in_any_log_term_was_created.