Cleanup: Pull some browser keep alive functions into its own file.

chrome/browser/browser_process_impl.cc

Index: chrome/browser/browser_process_impl.cc
diff --git a/chrome/browser/browser_process_impl.cc b/chrome/browser/browser_process_impl.cc
index 8d432d65c2ef858fd0da6fc759e1e4bb2a27bcca..11cfd294cf485a5d58b213cbb2c4ccc5207ff3fc 100644
--- a/chrome/browser/browser_process_impl.cc
+++ b/chrome/browser/browser_process_impl.cc
@@ -42,6 +42,7 @@
 #include "chrome/browser/intranet_redirect_detector.h"
 #include "chrome/browser/io_thread.h"
 #include "chrome/browser/lifetime/application_lifetime.h"
+#include "chrome/browser/lifetime/browser_keep_alive.h"
 #include "chrome/browser/metrics/chrome_metrics_service_accessor.h"
 #include "chrome/browser/metrics/metrics_services_manager.h"
 #include "chrome/browser/metrics/thread_watcher.h"
@@ -1233,7 +1234,8 @@ void BrowserProcessImpl::CacheDefaultWebClientState() {
 bool BrowserProcessImpl::CanAutorestartForUpdate() const {
   // Check if browser is in the background and if it needs to be restarted to
   // apply a pending update.
-  return chrome::GetTotalBrowserCount() == 0 && chrome::WillKeepAlive() &&
+  return chrome::GetTotalBrowserCount() == 0 &&
+         browser_lifetime::WillKeepAlive() &&
          upgrade_util::IsUpdatePendingRestart();
 }