Hint Rewrite @closed_wrt_map_subst using safe_auto_with_closed : subst.
Hint Rewrite @closed_wrt_subst using safe_auto_with_closed : subst.

Lemma closed_wrt_map_subst':
forall {A: Type} id e (Q: list (environ -> A)),
Forall (closed_wrt_vars (eq id)) Q ->
@map (LiftEnviron A) _ (subst id e) Q = Q.