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-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011     *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-Require Import BinPos Equalities Orders OrdersTac.
-
-Local Open Scope positive_scope.
-
-(** * DecidableType structure for [positive] numbers *)
-
-Module Positive_as_UBE <: UsualBoolEq.
- Definition t := positive.
- Definition eq := @eq positive.
- Definition eqb := Peqb.
- Definition eqb_eq := Peqb_eq.
-End Positive_as_UBE.
-
-Module Positive_as_DT <: UsualDecidableTypeFull
- := Make_UDTF Positive_as_UBE.
-
-(** Note that the last module fulfills by subtyping many other
-    interfaces, such as [DecidableType] or [EqualityType]. *)
-
-
-
-(** * OrderedType structure for [positive] numbers *)
-
-Module Positive_as_OT <: OrderedTypeFull.
- Include Positive_as_DT.
- Definition lt := Plt.
- Definition le := Ple.
- Definition compare p q := Pcompare p q Eq.
-
- Instance lt_strorder : StrictOrder Plt.
- Proof. split; [ exact Plt_irrefl | exact Plt_trans ]. Qed.
-
- Instance lt_compat : Proper (Logic.eq==>Logic.eq==>iff) Plt.
- Proof. repeat red; intros; subst; auto. Qed.
-
- Definition le_lteq := Ple_lteq.
- Definition compare_spec := Pcompare_spec.
-
-End Positive_as_OT.
-
-(** Note that [Positive_as_OT] can also be seen as a [UsualOrderedType]
-   and a [OrderedType] (and also as a [DecidableType]). *)
-
-
-
-(** * An [order] tactic for positive numbers *)
-
-Module PositiveOrder := OTF_to_OrderTac Positive_as_OT.
-Ltac p_order := PositiveOrder.order.
-
-(** Note that [p_order] is domain-agnostic: it will not prove
-    [1<=2] or [x<=x+x], but rather things like [x<=y -> y<=x -> x=y]. *)