simple induction 1; intros; auto with arith pts.
Qed.
End Inversion_Conv.
Hint Resolve chi_srt chi_ref chi_abs chi_app chi_prod: pts.
Hint Resolve inv_conv_conv: pts.
Section Head_Normal_Sorts.
Hypothesis sort_norm : forall (e : env) (s : sort), normal R e (Srt s).
Definition is_sort (t : term) :=
match t with
| Srt _ => True
| _ => False
end.

(* Specifications: *)
Lemma red_is_sort :
forall (e : env) (t u : term), red R e t u -> is_sort t -> is_sort u.