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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 check_valid_package(package,
                        cyg_arch='x86_64',
                        mirrors=None):
    '''
    Check if the package is valid on the given mirrors.

    Args:
        package: The name of the package
        cyg_arch: The cygwin architecture
        mirrors: any mirrors to check

    Returns (bool): True if Valid, otherwise False

    CLI Example:

    .. code-block:: bash

        salt '*' cyg.check_valid_package <package name>
    '''
    if mirrors is None:
        mirrors = [{DEFAULT_MIRROR: DEFAULT_MIRROR_KEY}]

    LOG.debug('Checking Valid Mirrors: %s', mirrors)

    for mirror in mirrors:
        for mirror_url, key in mirror.items():
            if package in _get_all_packages(mirror_url, cyg_arch):
                return True
    return False