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(*		Definition height         	  	 *)

Fixpoint height (t : avl_tree) : nat :=
  match t with
  | Avl_Nil => 0
  | Avl_Node _ _ l r _ => S (max (height l) (height r))
  end.

Lemma height_O_nil : forall t : avl_tree, height t = 0 -> t = Avl_Nil.