C# getter and setter shorthand

Question

If my understanding of the internal workings of this line is correct:

public int MyInt { get; set; }

Then it behind the scenes does this:

Answer 1

Create an IsDirty decorator (design pattern) to wrap some your properties requiring the isDirty flag functionality.

public class IsDirtyDecorator
{
    public bool IsDirty { get; private set; }

    private T _myValue;
    public T Value
    {
        get { return _myValue; }
        set { _myValue = value; IsDirty = true; }
    }
}

public class MyClass
{
    private IsDirtyDecorator MyInt = new IsDirtyDecorator();
    private IsDirtyDecorator MyString = new IsDirtyDecorator();

    public MyClass()
    {
        MyInt.Value = 123;
        MyString.Value = "Hello";
        Console.WriteLine(MyInt.Value);
        Console.WriteLine(MyInt.IsDirty);
        Console.WriteLine(MyString.Value);
        Console.WriteLine(MyString.IsDirty);
    }
}