Hint Extern 2 (closed_wrt_vars (eq _) (@eval_expr _ _)) => (apply closed_eval_expr_e; reflexivity) : closed.
Hint Extern 2 (closed_wrt_vars (eq _) (@eval_lvalue _ _)) => (apply closed_eval_lvalue_e; reflexivity) : closed.

Lemma closed_wrt_eval_expr: forall {cs: compspecs} S e,
expr_closed_wrt_vars S e ->
closed_wrt_vars S (eval_expr e).