Hint Resolve @closed_wrt_lift0C @closed_wrtl_lift0C: closed.

(* Specifications: *)
Lemma closed_wrt_lift1: forall {A}{B} S (f: A -> B) P,
closed_wrt_vars S P ->
closed_wrt_vars S (lift1 f P).
Lemma closed_wrtl_lift1: forall {A}{B} S (f: A -> B) P,
closed_wrt_lvars S P ->
closed_wrt_lvars S (lift1 f P).