simple induction 1; intros.
apply typ_sn with (Srt s); auto with arith pts.
red in |- *.
apply Acc_intro; intros.
inversion_clear H0.
elim shn_sort with e s (Srt s) y; auto with arith pts.
Qed.
Hint Resolve cumul_type_sn: pts.

(* Specifications: *)
Lemma subject_reduction_cumul : rule_sound cts_pts_functor (red hdr).
unfold red, hdr in |- *.