From 1a197792a437ca0a797c5dcec099d64b550028f8 Mon Sep 17 00:00:00 2001
From: letouzey
Date: Tue, 12 Jan 2010 15:50:01 +0000
Subject: Numbers/.../NDefOps: one more property about ltb

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12654 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Numbers/Natural/Abstract/NDefOps.v | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/theories/Numbers/Natural/Abstract/NDefOps.v b/theories/Numbers/Natural/Abstract/NDefOps.v
index 8ac7c6f6db..22eb2cb34a 100644
--- a/theories/Numbers/Natural/Abstract/NDefOps.v
+++ b/theories/Numbers/Natural/Abstract/NDefOps.v
@@ -176,6 +176,10 @@ intro n. rewrite ltb_0. split; intro H; [discriminate | false_hyp H nlt_0_r].
 intros n m. rewrite succ_ltb_mono. now rewrite <- succ_lt_mono.
 Qed.
 
+Theorem ltb_ge : forall n m, n << m = false <-> n >= m.
+Proof.
+intros. rewrite <- not_true_iff_false, ltb_lt. apply nlt_ge.
+Qed.
 
 (*****************************************************)
 (**                     Even                         *)
-- 
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