(* Commutation theorem *)

(* Specifications: *)
Lemma residuals_lift_rec :
forall U1 U2 U3 : redexes,
residuals U1 U2 U3 ->
forall k n : nat,
residuals (lift_rec_r U1 n k) (lift_rec_r U2 n k) (lift_rec_r U3 n k).
Lemma residuals_lift :
forall U1 U2 U3 : redexes,
residuals U1 U2 U3 ->
forall k : nat, residuals (lift_r k U1) (lift_r k U2) (lift_r k U3).