From d7e249dc1bfc2dd04ccf23c57b7ad40f1902568d Mon Sep 17 00:00:00 2001
From: emakarov
Date: Tue, 16 Oct 2007 16:28:17 +0000
Subject: Added transitivity and irreflexivity of <, as well as < -elimination
 for binary positive numbers.

Added directory contribs/micromega with the generalization of Frédéric Besson's micromega tactic for an arbitrary ordered ring. So far no tactic has been defined. One has to apply the theorems and find the certificate, which is necessary to solve inequations, manually.


git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10226 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Numbers/Integer/Binary/ZBinary.v | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

(limited to 'theories/Numbers/Integer/Binary')

diff --git a/theories/Numbers/Integer/Binary/ZBinary.v b/theories/Numbers/Integer/Binary/ZBinary.v
index cb8ac3b5b1..0a52d214a2 100644
--- a/theories/Numbers/Integer/Binary/ZBinary.v
+++ b/theories/Numbers/Integer/Binary/ZBinary.v
@@ -132,7 +132,14 @@ Qed.
 
 End NZOrdAxiomsMod.
 
-Definition Zopp := Zopp.
+Definition Zopp (x : Z) :=
+match x with
+| Z0 => Z0
+| Zpos x => Zneg x
+| Zneg x => Zpos x
+end.
+
+Notation "- x" := (Zopp x) : Z_scope.
 
 Add Morphism Zopp with signature NZE ==> NZE as Zopp_wd.
 Proof.
-- 
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