Fixpoint raw_elements_between (m: Raw.tree) : Raw.tree :=
  match m with
  | Raw.Leaf => Raw.Leaf
  | Raw.Node _ l x r =>
      if above_low_bound x then
        if below_high_bound x then
          Raw.join (raw_elements_between l) x (raw_elements_between r)
        else
          raw_elements_between l
      else
        raw_elements_between r
  end.Remark In_raw_elements_between_1:
  forall x m,
  Raw.In x (raw_elements_between m) -> Raw.In x m.

Lemma raw_elements_between_ok: forall m, Raw.bst m -> Raw.bst (raw_elements_between m).