insertAVLTree_ :: a (LH a) -> LH a | Eq, Ord a
insertAVLTree_ e (Leaf) = (Node 0 e Leaf Leaf)
insertAVLTree_ e (Node d x left right)
| e <= x    = repair1 (Node d x (insertAVLTree_ e left) right)
with repair1 newt =: (Node _ _ newl =: (Node _ r _ _) _)
        | depth newl - depth right <> 2 = newt
        | e < r = rotateR newt
        | otherwise = rotateRL newt
| otherwise = repair2 (Node d x left (insertAVLTree_ e right))
with repair2 newt =: (Node _ _ _ newr =: (Node _ r _ _))
        | depth newr - depth left <> 2 = newt
        | e > r = rotateL newt
        | otherwise = rotateLR newt