Proof using.
red. unfold in_any_log_term_was_created, 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.
iae_case; eauto.
- repeat find_higher_order_rewrite.
destruct_update; simpl in *;
find_apply_lem_hyp in_log;
eapply_prop_hyp in_any_log in_any_log;
break_exists_exists;
repeat find_higher_order_rewrite;
destruct_update; simpl in *; eauto.
- repeat find_reverse_rewrite.
find_eapply_lem_hyp in_aer; eauto.
eapply_prop_hyp in_any_log in_any_log;
break_exists_exists;
repeat find_higher_order_rewrite;
destruct_update; simpl in *; eauto.
- repeat find_higher_order_rewrite.
destruct_update; simpl in *;
find_eapply_lem_hyp in_ll; eauto;
eapply_prop_hyp in_any_log in_any_log;
break_exists_exists;
repeat find_higher_order_rewrite;
destruct_update; simpl in *; eauto.
Qed.

(* Specifications: *)
Lemma in_any_log_term_was_created_init :
refined_raft_net_invariant_init in_any_log_term_was_created.