Move assorted function in application_lifetime to where they are used.

chrome/browser/lifetime/application_lifetime.h

Index: chrome/browser/lifetime/application_lifetime.h
diff --git a/chrome/browser/lifetime/application_lifetime.h b/chrome/browser/lifetime/application_lifetime.h
index 3cf18549cd37768132f3af62cd9e806c18beded3..a0acd684dd30d3772a72643846c69bf9bf6917be 100644
--- a/chrome/browser/lifetime/application_lifetime.h
+++ b/chrome/browser/lifetime/application_lifetime.h
@@ -18,11 +18,6 @@ namespace chrome {
 // SIGTERM to start actual exit process.
 void AttemptUserExit();
 
-// Starts to collect shutdown traces. On ChromeOS this will start immediately
-// on AttemptUserExit() and all other systems will start once all tabs are
-// closed.
-void StartShutdownTracing();
-
 // Starts a user initiated restart process. On platforms other than
 // chromeos, this sets a restart bit in the preference so that
 // chrome will be restarted at the end of shutdown process. On
@@ -112,10 +107,6 @@ void OnAppExiting();
 // processing required.
 void HandleAppExitingForPlatform();
 
-// Returns true if we can start the shutdown sequence for the browser, i.e. the
-// last browser window is being closed.
-bool ShouldStartShutdown(Browser* browser);
-
 // Disable browser shutdown for unit tests.
 void DisableShutdownForTesting(bool disable_shutdown_for_testing);