data nomal-tree (A : Set) : Set where
  nleaf : (key : ℕ) → tree A
  nnode : (key : ℕ) → (lnode : nomal-tree A) → (rnode : nomal-tree A) → nomal-tree A

data meta-tree (A : Set) : (key : ℕ) → Set where
  mleaf : (key : ℕ) → meta-tree A key
  mnode : { l r : ℕ } → (key : ℕ) → (value : A)
    → (lnode : meta-tree A l)  → (rnode : meta-tree A r)
    → l ≤ key → key ≤ r → metatree A key