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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 _add_interval(all_intervals, new_interval):
 """ Adds a new interval to a set of none overlapping intervals. :param set[(int,int)] all_intervals: The set of distinct intervals. :param (int,int) new_interval: The new interval. """

        intervals = None
        old_interval = None
        for old_interval in all_intervals:
            intervals = Type2CondenseHelper._distinct(new_interval, old_interval)
            if intervals:
                break

        if intervals is None:
            all_intervals.add(new_interval)
        else:
            if old_interval:
                all_intervals.remove(old_interval)
            for distinct_interval in intervals:
                Type2CondenseHelper._add_interval(all_intervals, distinct_interval)