check if one set of types is a subset of the other

How can one check if one paramter pack (interpreted as a set) is a subset of another one?

So far I only have the frame (using std::tuple), but no functionality.

#include <tuple>
#include <type_traits>

template <typename, typename>
struct is_subset_of : std::false_type
{
};

template <typename ... Types1, typename ... Types2>
struct is_subset_of<std::tuple<Types1...>, std::tuple<Types2...>>
    : std::true_type
{
    // should only be true_type if Types1 is a subset of Types2
};

int main() {
    using t1 = std::tuple<int, double>;
    using t2 = std::tuple<double, int>;
    using t3 = std::tuple<int, double, char>;

    static_assert(is_subset_of<t1, t1>::value, "err");
    static_assert(is_subset_of<t1, t2>::value, "err");
    static_assert(is_subset_of<t2, t1>::value, "err");
    static_assert(is_subset_of<t2, t3>::value, "err");
    static_assert(!is_subset_of<t3, t2>::value, "err");
}

Every type is not allowed to occur more than once in a set.