Is there an equivalent of “None()” in LINQ?

None is the same as !Any, so you could define your own extension method as follows:

public static class EnumerableExtensions
{
    public static bool None<TSource>(this IEnumerable<TSource> source,
                                     Func<TSource, bool> predicate)
    {
        return !source.Any(predicate);
    }
}