#[global]
  Instance lt_strorder : StrictOrder lt.Local Instance compare_compat_1 : Proper (eq==>Logic.eq==>Logic.eq) compare.#[global]
  Instance compare_compat : Proper (eq==>eq==>Logic.eq) compare.Local Instance lt_compat : Proper (eq==>eq==>iff) lt.

Lemma exists_spec : forall s f, @compat_bool elt E.eq f -> (exists_ f s = true <-> Exists (fun x => f x = true) s).