simple induction 1; intros; auto with pts.
apply rt_step.
apply R_substs with (2 := H1); auto with pts.
apply rt_trans with (subst_rec s y n); auto with pts.
Qed.

(* Specifications: *)
Lemma R_rst_subst : R_subst (R_rst R).
unfold R_subst, R_rt in |- *.