intros.
apply conv_trans with (App u' v).
elim H; simpl in |- *; intros; auto with pts.
apply conv_trans with (App y v); auto with pts.
elim H0; intros; auto with pts.
apply conv_trans with (App u' y); auto with pts.
Qed.

Lemma conv_conv_prod :
forall (e : env) (A A' B B' : term),
conv e A A' -> conv (Ax A' :: e) B B' -> conv e (Prod A B) (Prod A' B').