Proof using.
intros n ln t l H; elim H; simpl in |- *; auto.
intros; discriminate.
intros n0 ln1 ln2 t1 t2 l1 l2 H0; case ln1; simpl in |- *; auto.
intros; discriminate.
Qed.

(* The cover list is never empty *)
Theorem height_pred_not_nil2 :
forall (n : nat) (ln : list nat) (t : btree A) (l : list (btree A)),
height_pred n ln l t -> l <> nil.