Section BasicProperties.
(** Some old specifications written with boolean equalities. *)
Variable s s' s'': t.
Variable x y z : elt.
(** properties of [mem] *)
(** Properties of [equal] *)
(* Properties of [subset] *)
(** Properties of [choose] *)
(** Properties of [add] *)

Lemma add_equal:
mem x s=true -> equal (add x s) s=true.