Hint Resolve @closed_wrt_lift3C @closed_wrtl_lift3C : closed.

(* Specifications: *)
Lemma closed_wrt_lift4: forall {A1 A2 A3 A4}{B} S (f: A1 -> A2 -> A3 -> A4 -> B)
P1 P2 P3 P4,
closed_wrt_vars S P1 ->
closed_wrt_vars S P2 ->
closed_wrt_vars S P3 ->
closed_wrt_vars S P4 ->
closed_wrt_vars S (lift4 f P1 P2 P3 P4).
Lemma closed_wrtl_lift4: forall {A1 A2 A3 A4}{B} S (f: A1 -> A2 -> A3 -> A4 -> B)
P1 P2 P3 P4,
closed_wrt_lvars S P1 ->
closed_wrt_lvars S P2 ->
closed_wrt_lvars S P3 ->
closed_wrt_lvars S P4 ->
closed_wrt_lvars S (lift4 f P1 P2 P3 P4).