From 6b649aba925b6f7462da07599fe67ebb12a3460e Mon Sep 17 00:00:00 2001
From: Samuel Mimram <samuel.mimram@ens-lyon.org>
Date: Wed, 28 Jul 2004 21:54:47 +0000
Subject: Imported Upstream version 8.0pl1

---
 theories/Bool/Zerob.v | 38 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 38 insertions(+)
 create mode 100755 theories/Bool/Zerob.v

(limited to 'theories/Bool/Zerob.v')

diff --git a/theories/Bool/Zerob.v b/theories/Bool/Zerob.v
new file mode 100755
index 00000000..b654e556
--- /dev/null
+++ b/theories/Bool/Zerob.v
@@ -0,0 +1,38 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(*i $Id: Zerob.v,v 1.8.2.1 2004/07/16 19:31:03 herbelin Exp $ i*)
+
+Require Import Arith.
+Require Import Bool.
+
+Open Local Scope nat_scope.
+
+Definition zerob (n:nat) : bool :=
+  match n with
+  | O => true
+  | S _ => false
+  end.
+
+Lemma zerob_true_intro : forall n:nat, n = 0 -> zerob n = true.
+destruct n; [ trivial with bool | inversion 1 ].
+Qed.
+Hint Resolve zerob_true_intro: bool.
+
+Lemma zerob_true_elim : forall n:nat, zerob n = true -> n = 0.
+destruct n; [ trivial with bool | inversion 1 ].
+Qed.
+
+Lemma zerob_false_intro : forall n:nat, n <> 0 -> zerob n = false.
+destruct n; [ destruct 1; auto with bool | trivial with bool ].
+Qed.
+Hint Resolve zerob_false_intro: bool.
+
+Lemma zerob_false_elim : forall n:nat, zerob n = false -> n <> 0.
+destruct n; [ intro H; inversion H | auto with bool ].
+Qed.
\ No newline at end of file
-- 
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