simple induction 1; intros; auto with pts.
apply rt_step.
apply R_lifts with (2 := H1); auto with pts.
apply rt_trans with (lift_rec 1 y k); auto with pts.
Qed.

(* Specifications: *)
Lemma R_rst_lift : R_lift (R_rst R).
unfold R_lift, R_rst in |- *.