Proxy Design Patterns in C#

Proxy   (MathProxy)
maintains a reference that lets the proxy access the real subject. Proxy may refer to a Subject if the RealSubject and Subject interfaces are the same.
provides an interface identical to Subject's so that a proxy can be substituted for for the real subject.
controls access to the real subject and may be responsible for creating and deleting it.
other responsibilites depend on the kind of proxy:
remote proxies are responsible for encoding a request and its arguments and for sending the encoded request to the real subject in a different address space.
virtual proxies may cache additional information about the real subject so that they can postpone accessing it. For example, the ImageProxy from the Motivation caches the real images's extent.
protection proxies check that the caller has the access permissions required to perform a request.
Subject   (IMath)
defines the common interface for RealSubject and Proxy so that a Proxy can be used anywhere a RealSubject is expected.
RealSubject   (Math)
defines the real object that the proxy represents.

class Program
    {
        static void Main(string[] args)
        {
            Proxy proxy = new Proxy();
            proxy.Request();

            Console.ReadKey();
        }
    }

    abstract class Subject
    {
        public abstract void Request();
    }
    class RealSubject : Subject
    {
        public override void Request()
        {
            Console.WriteLine("Called RealSubject.Request()");
        }
    }

    class Proxy : Subject
    {
        private RealSubject _realSubject = null;
        public override void Request()
        {
            //Use lazy initialization
            if (_realSubject == null)
                _realSubject = new RealSubject();
            _realSubject.Request();
        }
    }