Hint Resolve closed_wrtl_eval_var : closed.
(* Lemma closed_wrt_var: forall S id t v, closed_wrt_vars S (var id t v). Hint Resolve closed_wrt_var : closed.  Lemma closed_wrtl_var: forall S id t v, ~ S id -> closed_wrt_lvars S (var id t v). Hint Resolve closed_wrtl_var : closed. *)

Lemma closed_wrt_lvar:
forall S id t v, closed_wrt_vars S (locald_denote (lvar id t v)).