intros t avl_t.
elim avl_t.
simpl in |- *; trivial.
intros k d l r b avl_l ih_l avl_r ih_r Balanced_t below_l above_r.
clear avl_l avl_r below_l above_r.
simpl in |- *.
rewrite <- ih_l.
rewrite <- ih_r.
clear ih_l ih_r.
inversion_clear Balanced_t.
rewrite H.
rewrite (max_Sn_n (height_avl r)).
trivial.
rewrite H.
rewrite (max_n_n (height_avl r)).
trivial.
rewrite <- H.
rewrite (max_n_Sn (height_avl l)).
trivial.
Qed.

Lemma is_balanced_avl_is_balanced :
forall l r : avl_tree,
is_avl l ->
is_avl r -> forall b : bal, is_balanced_avl l r b -> is_balanced l r b.