Concept checking using ranges-v3 library - c++

Question

In this blog post, I saw Eric Niebler explaining his take on concept checking. It looked like a nice balance between simplicity and practicality for me so I wanted to give it a try.
To test things myself, I came up with a quick concept of vector spaces. Here is the code:
#include <range/v3/utility/concepts.hpp>
#include <array>
#include <algorithm>
#include <string>
struct vector_space
{
// Valid expressions
template<typename Field, typename Vector>
auto requires(Field &&f, Vector &&v1, Vector &&v2) -> decltype(
ranges::concepts::valid_expr(
f * v1,
v1 + v2
));
};
template<typename Field, typename Vector>
constexpr bool VectorSpace()
{
return ranges::concepts::models<vector_space, Field, Vector>();
}
template<typename Field, typename Vector,
CONCEPT_REQUIRES_(VectorSpace<Field, Vector>())>
void linear_comb(Field f1, Vector v1, Field f2, Vector v2)
{
return (f1 * v1) + (f2 * v2);
}
template <typename T, std::size_t dim>
std::array<T, dim> operator+(std::array<T, dim> const& a1,
std::array<T, dim> const& a2) {
std::array<T, dim> res;
std::transform(a1.begin(), a1.end(), a2.begin(),
res.begin(),
[](T const& e1, T const& e2) {
return e1 + e2;
});
return res;
}
template <typename Field, typename T, std::size_t dim>
std::array<T, dim> operator*(std::array<T, dim> const& a,
Field f) {
std::array<T, dim> res;
std::transform(a.begin(), a.end(),
res.begin(),
[f](T const& e) {
return f * e;
});
return res;
}
template <typename Field, typename T, std::size_t dim>
std::array<T, dim> operator*(Field f, std::array<T, dim> const& a) {
return a * f;
}
int main() {
std::string s1 = "hello";
std::string s2 = "world";
std::array<float, 4> a1{1.1f, 2.2f, 3.3f, 4.4f};
std::array<float, 4> a2{4.4f, 3.3f, 2.2f, 1.1f};
std::array<float, 4> a3 = (3.14f * a1) + (2.71f * a2);
linear_comb(3.14f, a1, 2.71f, a2);
}
As you can see, I want to check that given v1, v2 of Vector and f of Field, expressions f * v1 and v1 + v2 to make sense. In short, I want scalar multiplication and vector addition. Although I can correctly compute a3 in main, function linear_comb tells me that concept VectorSpace<Field, Vector> is not satisfied. It correctly deduces Field as float and Vector as std::array<float, 4>. Why is it not seeing above as valid expressions then?