Hint Resolve closed_wrt_lift2 closed_wrtl_lift2 : closed.

Lemma closed_wrt_lift2C: 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 (@liftx (Tarrow A1 (Tarrow A2 (LiftEnviron B))) f P1 P2).