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] *)

Lemma add_spec: forall s x y, In y (add x s) <-> y=x \/ In y s.