intros bs H'; elim H'; auto.
intros l H'0 us H'1 H'2.
apply lem1; auto.
rewrite <- H'1; auto.
intros l H'0 H'1 us H'2 H'3; red in |- *.
apply OpenInd with (lt := prod_lt); auto.
exact WFlem1.
intros a H'4.
apply H'1 with (a := snd a); auto.
rewrite H'2; auto.
Qed.

Lemma keylem_cor : WR (A * B) (ProdRel A B leq R).
red in |- *; apply keylem with (bs := nil (A:=B)); auto.