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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 SetoidList Morphisms OrdersTac.
Set Implicit Arguments.
Unset Strict Implicit.
(** NB: This file is here only for compatibility with earlier version of [FSets] and [FMap]. Please use [Structures/Orders.v] directly now. *)
(** * Ordered types *)
Inductive Compare (X : Type) (lt eq : X -> X -> Prop) (x y : X) : Type :=
| LT : lt x y -> Compare lt eq x y
| EQ : eq x y -> Compare lt eq x y
| GT : lt y x -> Compare lt eq x y.
Arguments LT [X lt eq x y] _.
Arguments EQ [X lt eq x y] _.
Arguments GT [X lt eq x y] _.
Create HintDb ordered_type.
Module Type MiniOrderedType.
Parameter Inline t : Type.
Parameter Inline eq : t -> t -> Prop.
Parameter Inline lt : t -> t -> Prop.

(* Specifications: *)
Axiom eq_refl : forall x : t, eq x x.
Axiom eq_sym : forall x y : t, eq x y -> eq y x.
Axiom eq_trans : forall x y z : t, eq x y -> eq y z -> eq x z.
Axiom lt_trans : forall x y z : t, lt x y -> lt y z -> lt x z.
Axiom lt_not_eq : forall x y : t, lt x y -> ~ eq x y.
Parameter compare : forall x y : t, Compare lt eq x y.