Definition elements (i: interv) : list Z :=
  elements_rec (fst i) (snd i).

(* Specifications: *)
Lemma in_elements: forall x i, In x i -> List.In x (elements i).
Lemma elements_in: forall x i, List.In x (elements i) -> In x i.
Lemma in_elements: forall x i, In x i -> List.In x (elements i).
Lemma elements_in: forall x i, List.In x (elements i) -> In x i.