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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def get_stop_times(feed: "Feed", date: Optional[str] = None) -> DataFrame: """ Return a subset of ``feed.stop_times``. Parameters feed : Feed date : string YYYYMMDD date string restricting the output to trips active on the date Returns ------- DataFrame Subset of ``feed.stop_times`` Notes ----- Assume the following feed attributes are not ``None``: - ``feed.stop_times`` - Those used in :func:`.trips.get_trips` """

    f = feed.stop_times.copy()
    if date is None:
        return f

    g = feed.get_trips(date)
    return f[f["trip_id"].isin(g["trip_id"])]