End lt_spec.
#[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.
(** Specification of [add] *)

(** Specification of [fold] *)
Lemma fold_spec: forall s (A : Type) (i : A) (f : elt -> A -> A),
fold f s i = fold_left (fun a e => f e a) (elements s) i.