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] *)
(** Properties of [remove] *)
(** Properties of [is_empty] *)
(** Properties of [singleton] *)

Lemma singleton_mem_2: ~E.eq x y -> mem y (singleton x)=false.