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.
simple induction 1; auto with arith pts.
simple destruct x; simpl in |- *; intros.
inversion_clear H0; simpl in |- *; auto with arith pts.
elim sort_norm with e s y; auto with arith pts.
elim H1.
elim H1.
elim H1.
elim H1.
Qed.
simple destruct t; simpl in |- *; auto with arith pts; intros; elim H.
Qed.

Lemma hn_sort : forall (e : env) (s : sort), head_normal R e (Srt s).