Can non-nullable references be implemented as a library?

[Denis Koroskin]

Since many people think that non-nullable references can be implemented as  
a library and thus don't belong to core language, I've decided to show  
that it is in fact impossible to do so.

How do you enforce the following behavior:
class Foo
{
    this()
    {
        // error: variable nonNull not initialized
    }

    this()
    {
        nonNull.someMethod(); // error: variable used before initialized
        auto s = toString(); // error: can't call any methods before  
initialized

        nonNull = new Bar();
        s = toString(); // okay
    }

    string toString() { return nonNull.toString(); }

    NonNull!(Bar) nonNull;
}

class Bar : Foo
{
    this()
    {
        nonNull.someMethod(); // error: variable used before initialized

        super(); // initializes nonNull
        nonNull.someMethod(); // fine
    }
}

Without support of these use-cases NonNull!(T) is useless.

There can be other examples, but I think these are enough to prove that  
non-nullable references can not be implemented in library.