AVL Tree - Print ascending using in-order
AVL trees, like all other binary search trees, have the following guarantee:


  Suppose that $v$ is a node with left child $l$ and right child $r$. If $x$ is a node in the subtree rooted at $l$ and $y$ is a node in the subtree rooted at $r$ then $key(x) \leq key(v) \leq key(y)$.


Using this, you can easily prove by induction that the inorder traversal of a binary search three produces a list of keys in nondecreasing order.