def intersect_incomparable_lists(superset, subset, name_map: dict) ->list:
    """
    Function for identifying the intersection of two lists by
    using a proxy identifier (alt_name) for elements in superset.

    :param superset: A list or set of strings
    :param subset: A list or set of strings
    :param name_map: A dictionary whose keys are in superset and values are in subset
    :return: A list of strings that are in both superset and subset
    """
    intersection = list()
    for seq_name in superset:
        alt_name = name_map[seq_name]
        if alt_name in subset:
            intersection.append(seq_name)
    return intersection
