From 06a2c96d8489f3ab57956c193456a2b394c1ca06 Mon Sep 17 00:00:00 2001
From: herbelin
Date: Tue, 11 Aug 2009 10:29:45 +0000
Subject: Fixed extra space in printing notation { x & P } + minor other things
 (shorter proof of O_S in trunk + typo).

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12271 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Init/Notations.v | 8 ++++----
 theories/Init/Peano.v     | 3 +--
 theories/ZArith/Zbool.v   | 4 ++--
 3 files changed, 7 insertions(+), 8 deletions(-)

diff --git a/theories/Init/Notations.v b/theories/Init/Notations.v
index c4780ace52..0c628298dc 100644
--- a/theories/Init/Notations.v
+++ b/theories/Init/Notations.v
@@ -68,13 +68,13 @@ Reserved Notation "{ x }" (at level 0, x at level 99).
 (** Notations for sigma-types or subsets *)
 
 Reserved Notation "{ x  |  P }" (at level 0, x at level 99).
-Reserved Notation "{ x  |  P  &  Q }" (at level 0, x at level 99).
+Reserved Notation "{ x  |  P  & Q }" (at level 0, x at level 99).
 
 Reserved Notation "{ x : A  |  P }" (at level 0, x at level 99).
-Reserved Notation "{ x : A  |  P  &  Q }" (at level 0, x at level 99).
+Reserved Notation "{ x : A  |  P  & Q }" (at level 0, x at level 99).
 
-Reserved Notation "{ x : A  &  P }" (at level 0, x at level 99).
-Reserved Notation "{ x : A  &  P  &  Q }" (at level 0, x at level 99).
+Reserved Notation "{ x : A  & P }" (at level 0, x at level 99).
+Reserved Notation "{ x : A  & P  & Q }" (at level 0, x at level 99).
 
 Delimit Scope type_scope with type.
 Delimit Scope core_scope with core.
diff --git a/theories/Init/Peano.v b/theories/Init/Peano.v
index 322a25468a..9924d8a658 100644
--- a/theories/Init/Peano.v
+++ b/theories/Init/Peano.v
@@ -77,8 +77,7 @@ Definition IsSucc (n:nat) : Prop :=
 
 Theorem O_S : forall n:nat, 0 <> S n.
 Proof.
-  unfold not; intros n H.
-  inversion H.
+  discriminate.
 Qed.
 Hint Resolve O_S: core.
 
diff --git a/theories/ZArith/Zbool.v b/theories/ZArith/Zbool.v
index cce0438fa6..5aab73f2e0 100644
--- a/theories/ZArith/Zbool.v
+++ b/theories/ZArith/Zbool.v
@@ -18,9 +18,9 @@ Require Import Sumbool.
 Unset Boxed Definitions.
 Open Local Scope Z_scope.
 
-(** * Boolean operations from decidabilty of order *)
+(** * Boolean operations from decidability of order *)
 (** The decidability of equality and order relations over
-    type [Z] give some boolean functions with the adequate specification. *)
+    type [Z] gives some boolean functions with the adequate specification. *)
 
 Definition Z_lt_ge_bool (x y:Z) := bool_of_sumbool (Z_lt_ge_dec x y).
 Definition Z_ge_lt_bool (x y:Z) := bool_of_sumbool (Z_ge_lt_dec x y).
-- 
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