Hint Rewrite @subst_eval_expr_eq @subst_eval_lvalue_eq : subst.

(* Specifications: *)
Lemma closed_wrt_subst:
forall {A} id e (P: environ -> A), closed_wrt_vars (eq id) P -> subst id e P = P.
Lemma closed_wrt_map_subst:
forall {A: Type} id e (Q: list (environ -> A)),
Forall (closed_wrt_vars (eq id)) Q ->
map (subst id e) Q = Q.