[Mac] During shutdown, do not post NSApplicationWillTerminateNotification twice.

chrome/browser/chrome_browser_application_mac.mm

 // Copyright (c) 2012 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #import "chrome/browser/chrome_browser_application_mac.h"
 
 #import "base/auto_reset.h"
 #import "base/logging.h"
 #include "base/mac/crash_logging.h"
 #import "base/mac/scoped_nsexception_enabler.h"
@@ skipping 313 matching lines @@
 //
 // |-tryToTerminateApplication:| differs from the standard
 // |-applicationShouldTerminate:| in that no special event loop is run in the
 // case that immediate termination is not possible (e.g., if dialog boxes
 // allowing the user to cancel have to be shown). Instead, this method sets a
 // flag and tries to close all browsers. This flag causes the closure of the
 // final browser window to begin actual tear-down of the application.
 // Termination is cancelled by resetting this flag. The standard
 // |-applicationShouldTerminate:| is not supported, and code paths leading to it
 // must be redirected.
+//
+// When the last browser has been destroyed, the BrowserList calls
+// browser::OnAppExiting(), which is the point of no return. That will cause
+// the NSApplicationWillTerminateNotification to be posted, which ends the
+// NSApplication event loop, so final post- MessageLoop::Run() work is done
+// before exiting.
 - (void)terminate:(id)sender {
   AppController* appController = static_cast<AppController*>([NSApp delegate]);
-  if ([appController tryToTerminateApplication:self]) {
-    [[NSNotificationCenter defaultCenter]
-        postNotificationName:NSApplicationWillTerminateNotification
-                      object:self];
-  }
-
+  [appController tryToTerminateApplication:self];
   // Return, don't exit. The application is responsible for exiting on its own.
 }
 
 - (void)cancelTerminate:(id)sender {
   AppController* appController = static_cast<AppController*>([NSApp delegate]);
   [appController stopTryingToTerminateApplication:self];
 }
 
 - (BOOL)sendAction:(SEL)anAction to:(id)aTarget from:(id)sender {
   // The Dock menu contains an automagic section where you can select
@@ skipping 222 matching lines @@
   std::vector<NSWindow*>::iterator window_iterator =
       std::find(previousKeyWindows_.begin(),
                 previousKeyWindows_.end(),
                 window);
   if (window_iterator != previousKeyWindows_.end()) {
     previousKeyWindows_.erase(window_iterator);
   }
 }
 
 @end