diff options
author | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:02:20 +0100 |
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committer | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:02:20 +0100 |
commit | 97fefe1fcca363a1317e066e7f4b99b9c1e9987b (patch) | |
tree | 97ec6b7d831cc5fb66328b0c63a11db1cbb2f158 /theories/NArith/POrderedType.v | |
parent | 300293c119981054c95182a90c829058530a6b6f (diff) |
Imported Upstream version 8.4~betaupstream/8.4_beta
Diffstat (limited to 'theories/NArith/POrderedType.v')
-rw-r--r-- | theories/NArith/POrderedType.v | 60 |
1 files changed, 0 insertions, 60 deletions
diff --git a/theories/NArith/POrderedType.v b/theories/NArith/POrderedType.v deleted file mode 100644 index 0ff03c31..00000000 --- a/theories/NArith/POrderedType.v +++ /dev/null @@ -1,60 +0,0 @@ -(************************************************************************) -(* 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]. *) |