def min_gt(seq, val):
    """
    Return smallest item in seq for which item > val applies.
    None is returned if seq was empty or all items in seq were <= val.

    >>> min_gt([1, 3, 6, 7], 4)
    6
    >>> min_gt([2, 4, 7, 11], 5)
    7
    """

    for v in seq:
        if v > val:
            return v
    return None