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] *)

Lemma choose_mem_3:
is_empty s=false -> {x:elt|choose s=Some x /\ mem x s=true}.