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(*         *      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)         *)
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Require Export RelationPairs SetoidList Orders EqualitiesFacts.
Set Implicit Arguments.
Unset Strict Implicit.
(** * Specialization of results about lists modulo. *)
Module OrderedTypeLists (O:OrderedType).
Local Notation In:=(InA O.eq).
Local Notation Inf:=(lelistA O.lt).
Local Notation Sort:=(sort O.lt).
Local Notation NoDup:=(NoDupA O.eq).

Lemma In_eq : forall l x y, eq x y -> In x l -> In y l.