Lemma bxorlist_app xs2 ys2: forall xs1 ys1 zs1 zs2, bxorlist xs1 ys1 = Some zs1 -> bxorlist xs2 ys2 = Some zs2 -> bxorlist (xs1 ++ xs2) (ys1 ++ ys2) = Some(zs1 ++ zs2).