(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
(** * Finite sets library : conversion to old [Finite_sets] *)
(** * Going from [MSets] with usual Leibniz equality to the good old [Ensembles] and [Finite_sets] theory. *)
Module WS_to_Finite_set (U:UsualDecidableType)(M: WSetsOn U).
Module MP:= WPropertiesOn U M.
Definition mkEns : M.t -> Ensemble M.elt :=
fun s x => M.In x s.
Notation " !! " := mkEns.

Lemma singleton_Singleton : forall x, !!(M.singleton x) === Singleton _ x .