induction l1 as [| a1 l1 IH].
intros H; case H; auto.
intros _ Hl2.
case (list_case _ l1); intros; subst; simpl app; rewrite joinlS; auto.
rewrite joinlS, IH, join_assoc; auto.
destruct l1; auto; try (intros; discriminate).
Qed.

Lemma joinl0_base1_perm n l1 l2 : perm l1 l2 ->
(forall x, In x l1 -> cbl _ (base n 1) x) -> joinl n l1 = 0 -> joinl n l2 = 0.