Hint Resolve closed_wrt_lift1 closed_wrtl_lift1 : closed.

(* Specifications: *)
Lemma closed_wrt_lift1C: forall {A}{B} S (f: A -> B) P,
closed_wrt_vars S P ->
closed_wrt_vars S (@liftx (Tarrow A (LiftEnviron B)) f P).
Lemma closed_wrtl_lift1C: forall {A}{B} S (f: A -> B) P,
closed_wrt_lvars S P ->
closed_wrt_lvars S (@liftx (Tarrow A (LiftEnviron B)) f P).