Hint Resolve @closed_wrt_lift1C @closed_wrtl_lift1C : closed.

(* Specifications: *)
Lemma closed_wrt_lift2: forall {A1 A2}{B} S (f: A1 -> A2 -> B) P1 P2,
closed_wrt_vars S P1 ->
closed_wrt_vars S P2 ->
closed_wrt_vars S (lift2 f P1 P2).
Lemma closed_wrtl_lift2: forall {A1 A2}{B} S (f: A1 -> A2 -> B) P1 P2,
closed_wrt_lvars S P1 ->
closed_wrt_lvars S P2 ->
closed_wrt_lvars S (lift2 f P1 P2).