diff options
Diffstat (limited to 'theories/NArith/NOrderedType.v')
-rw-r--r-- | theories/NArith/NOrderedType.v | 60 |
1 files changed, 0 insertions, 60 deletions
diff --git a/theories/NArith/NOrderedType.v b/theories/NArith/NOrderedType.v deleted file mode 100644 index f1ab4b23..00000000 --- a/theories/NArith/NOrderedType.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 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]. *) - |