Hint Resolve closed_wrt_lift3 closed_wrtl_lift3 : closed.

(* Specifications: *)
Lemma closed_wrt_lift3C: forall {A1 A2 A3}{B} S (f: A1 -> A2 -> A3 -> B) P1 P2 P3,
closed_wrt_vars S P1 ->
closed_wrt_vars S P2 ->
closed_wrt_vars S P3 ->
closed_wrt_vars S (@liftx (Tarrow A1 (Tarrow A2 (Tarrow A3 (LiftEnviron B)))) f P1 P2 P3).
Lemma closed_wrtl_lift3C: forall {A1 A2 A3}{B} S (f: A1 -> A2 -> A3 -> B) P1 P2 P3,
closed_wrt_lvars S P1 ->
closed_wrt_lvars S P2 ->
closed_wrt_lvars S P3 ->
closed_wrt_lvars S (@liftx (Tarrow A1 (Tarrow A2 (Tarrow A3 (LiftEnviron B)))) f P1 P2 P3).