intros.
inversion H; assumption.
Qed.

Lemma hasnot_grown_left__preserves_is_balanced_avl :
forall (l l0 r0 : avl_tree) (b0 : bal),
is_balanced_avl l0 r0 b0 ->
height_avl l = height_avl l0 -> is_balanced_avl l r0 b0.