intros l r k d b avl_t.
apply is_balanced_avl_is_balanced.
apply (inv_is_avl_left k d l r b avl_t).
apply (inv_is_avl_right k d l r b avl_t).
apply (inv_is_avl_is_balanced_avl k d l r b avl_t).
Qed.

Lemma is_below_avl_is_below :
forall t : avl_tree,
is_avl t -> forall k0 : Int, is_below_avl t k0 -> is_below t k0.