apply sort_is_norm.
apply red_is_sort with e (Srt s); simpl in |- *; auto with arith pts.
Qed.
End Head_Normal_Sorts.
Section Head_Normal_Products.
Hypothesis prod_norm : forall (e : env) (A B : term), normal R e (Prod A B).
Definition is_prod (t : term) :=
match t with
| Prod _ _ => True
| _ => False
end.

Lemma red_is_prod :
forall (e : env) (t u : term), red R e t u -> is_prod t -> is_prod u.