If an application is filed, and proceedings for the formation of the district are commenced and prosecuted, in the manner and within the time specified by this part, the inclusion within the boundaries of the proposed district of territory formed into a new city or annexed to an existing city, pursuant to proceedings which were not commenced by the filing of a valid petition prior to the approval of the application, shall not prevent or invalidate the formation of the district even though the remainder of the corporate area of the city is not included in the district.