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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *)
(* \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_DT <: UsualDecidableTypeFull := Pos.
(** 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 := Pos.
(** 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]. *)
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