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Diffstat (limited to 'theories/PArith/POrderedType.v')
-rw-r--r-- | theories/PArith/POrderedType.v | 36 |
1 files changed, 36 insertions, 0 deletions
diff --git a/theories/PArith/POrderedType.v b/theories/PArith/POrderedType.v new file mode 100644 index 00000000..4aae6271 --- /dev/null +++ b/theories/PArith/POrderedType.v @@ -0,0 +1,36 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) +(* \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]. *) |