Inner member function template definition with (non-type) enum argument

I'm having difficulty defining and specializing a member function of an update()inner class Outer<T1>::Inner, which is the template for the non-type (enum) argument.

#include <cstdlib>

template<typename T1>
struct Outer
{
    struct Inner
    {
        enum Type{ A , B , C };

        template<Type T2>
        void update();
    };
};

// Definition
template<typename T1>
template<Outer<T1>::Inner::Type T2>
void Outer<T1>::Inner::update()
{
}

// Specialization
template<typename T1>
template<Outer<T1>::Inner::A >
void Outer<T1>::Inner::update()
{
}

int main()
{
    return EXIT_SUCCESS;
}

I get the following error message in GCC 4.5.3

prog.cpp:17:28: error: ‘Outer::Inner::Type’ is not a type
prog.cpp:18:6: error: prototype for ‘void Outer<T1>::Inner::update()’ does not match any in class ‘Outer<T1>::Inner’
prog.cpp:11:15: error: candidate is: template<class T1> template<Outer<T1>::Inner::Type T2> void Outer<T1>::Inner::update()
prog.cpp:24:28: error: ‘Outer::Inner::A’ is not a type
prog.cpp:25:6: error: prototype for ‘void Outer<T1>::Inner::update()’ does not match any in class ‘Outer<T1>::Inner’
prog.cpp:11:15: error: candidate is: template<class T1> template<Outer<T1>::Inner::Type T2> void Outer<T1>::Inner::update()

BTW, unlike GCC, Visual Studio 2008 cannot compile the following

template<typename T1>
struct Outer
{
    struct Inner
    {
        enum Type{ A , B , C };

        template<Type T2>
        struct Deep;
    };
};

template<typename T1>
template<typename Outer<T1>::Inner::Type T2>
struct Outer<T1>::Inner::Deep
{
};