Hint Resolve @closed_wrt_lift2C @closed_wrtl_lift2C : closed.

(* Specifications: *)
Lemma closed_wrt_lift3: 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 (lift3 f P1 P2 P3).
Lemma closed_wrtl_lift3: 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 (lift3 f P1 P2 P3).