Module E := D.Definition compare (s s':t) := M.compare s s'.Definition min_elt (s:t) : option elt := M.min_elt s.Definition max_elt (s:t) : option elt := M.max_elt s.Definition lt (s s':t) := M.lt s s'.(** Specification of [lt] *)
#[global]
  Instance lt_strorder : StrictOrder lt.#[global]
  Instance lt_compat : Proper (eq==>eq==>iff) lt.

Lemma max_elt_spec2 : max_elt s = Some x -> In y s -> ~ O.lt x y.