simple induction 1; intros.
apply wft_typed with s.
apply subject_reduction_cumul with T0; auto with arith pts.
cut (conv_hn_inv hd_rule e (Srt s) U); intros.
inversion_clear H1; auto with arith pts.
apply inv_red_hn; auto with arith pts.
Qed.

(* Specifications: *)
Lemma cumul_least_sort :
forall (e : env) (t : term),
wf_type cts_pts_functor e t -> red_to_sort_dec cts_pts_functor e t.