simple induction 1; auto with arith pts.
simple destruct x; simpl in |- *; intros.
inversion_clear H0; simpl in |- *; auto with arith pts.
elim H1.
elim H1.
elim H1.
elim H1.
inversion_clear H0; simpl in |- *; auto with arith pts.
elim prod_norm with e t0 t1 y; auto with arith pts.
Qed.

Lemma prod_is_norm : forall (e : env) (t : term), is_prod t -> normal R e t.
simple destruct t; simpl in |- *; auto with arith pts; intros; elim H.