intros.
cut (conv_hn_inv e (Prod A B) (Prod C D)); intros.
inversion_clear H0; auto with arith pts.
apply inv_conv_hn with (Prod A B) (Prod C D); auto with arith pts.
apply hn_prod.
apply hn_prod.
Qed.

Lemma inv_prod : product_inversion (conv R).
apply Build_product_inversion; intros.