How to redefine a property in C# through interface inheritance?

I have an interface 'IBase' that specifies a nullable int. A later interface 'IDerived' hides the nullable int and 'redefines' it as non-nullable.

interface IBase
{
    int? Redefineable { get; set; }
}

interface IDerived : IBase
{
    new int Redefineable { get; set; }
}

The class that implements these interfaces must explicitly implement the hidden property, however it's private so the client can't see it.

class TheClass : IDerived
{
    public int Redefineable { get; set; }
    int? IBase.Redefineable { get; set; }
}

However, even though it's a private property, I can still access it through the IBase interface!

var o = new TheClass();
o.Redefineable = 1; // ok

var hack = o as IBase;
hack.Redefineable = null; // uh!

This seems like some kind of violation of C# access modifiers, but either way it isn't really what I had in mind for redefining (not just hiding) a property. It's correct in the sense that it does what you're asking, get an IBase interface which has a nullable int but this is non-intuitive to the client who could then modify the wrong version of the property.

What I really want, is that if the client accesses IBase.Redefinable, then it behaves as if it's accessing the IDerived.Redefinable property, the 'real' property of TheClass. That way it's actually redefined, as in back through the hierarchy.

class TheClass : IDerived
{
    public int Redefineable { get; set; }
    int? IBase.Redefineable { 
        get { 
            // redirect to redefined property
            return this.Redefineable; 
        }
        set
        {
            // stop client setting it to null
            if (!value.HasValue)
                throw new InvalidOperationException();

            // redirect to redefined property
            this.Redefineable = value.Value;
        }
    }
}

This just feels like a hack, almost as if I'm missing something, so I want to ask if anyone knows a better/alternative way to implement re-definable properties?