Hint Resolve closed_wrt_eval_id closed_wrtl_eval_id : closed.

(* Specifications: *)
Lemma closed_wrt_temp: forall S i v,
~ S i -> closed_wrt_vars S (locald_denote (temp i v)).
Lemma closed_wrtl_temp: forall S i v,
closed_wrt_lvars S (locald_denote (temp i v)).