apply prod_is_norm.
apply red_is_prod with e (Prod A B); simpl in |- *; auto with arith pts.
Qed.

Lemma inv_R_prod :
forall (e : env) (A B C D : term),
conv R e (Prod A B) (Prod C D) -> conv R e C A /\ conv R (Ax C :: e) B D.