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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+Require Import BinNat Equalities Orders OrdersTac.
+
+Local Open Scope N_scope.
+
+(** * DecidableType structure for [N] binary natural numbers *)
+
+Module N_as_UBE <: UsualBoolEq.
+ Definition t := N.
+ Definition eq := @eq N.
+ Definition eqb := Neqb.
+ Definition eqb_eq := Neqb_eq.
+End N_as_UBE.
+
+Module N_as_DT <: UsualDecidableTypeFull := Make_UDTF N_as_UBE.
+
+(** Note that the last module fulfills by subtyping many other
+    interfaces, such as [DecidableType] or [EqualityType]. *)
+
+
+
+(** * OrderedType structure for [N] numbers *)
+
+Module N_as_OT <: OrderedTypeFull.
+ Include N_as_DT.
+ Definition lt := Nlt.
+ Definition le := Nle.
+ Definition compare := Ncompare.
+
+ Instance lt_strorder : StrictOrder Nlt.
+ Proof. split; [ exact Nlt_irrefl | exact Nlt_trans ]. Qed.
+
+ Instance lt_compat : Proper (Logic.eq==>Logic.eq==>iff) Nlt.
+ Proof. repeat red; intros; subst; auto. Qed.
+
+ Definition le_lteq := Nle_lteq.
+ Definition compare_spec := Ncompare_spec.
+
+End N_as_OT.
+
+(** Note that [N_as_OT] can also be seen as a [UsualOrderedType]
+   and a [OrderedType] (and also as a [DecidableType]). *)
+
+
+
+(** * An [order] tactic for [N] numbers *)
+
+Module NOrder := OTF_to_OrderTac N_as_OT.
+Ltac n_order := NOrder.order.
+
+(** Note that [n_order] is domain-agnostic: it will not prove
+    [1<=2] or [x<=x+x], but rather things like [x<=y -> y<=x -> x=y]. *)
+