Proof using.
red. intros. unfold in_any_log_term_was_created. intros.
match goal with
| H : nwState ?net ?h = (?gd, ?d) |- _ =>
replace gd with (fst (nwState net h)) in * by (rewrite H; reflexivity);
replace d with (snd (nwState net h)) in * by (rewrite H; reflexivity);
clear H
end.
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_eapply_lem_hyp doGenericServer_log; eauto.
repeat find_rewrite. eauto.
- find_apply_hyp_hyp. intuition; eauto.
do_in_map. subst. simpl in *.
find_apply_lem_hyp doGenericServer_packets. subst.
simpl in *. intuition.
- repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
Qed.

(* Specifications: *)
Lemma in_any_log_term_was_created_state_same_packet_subset :
refined_raft_net_invariant_state_same_packet_subset in_any_log_term_was_created.