I don't believe that you can prove this contention.
It's not all that difficult to prove, actually. Go back to the 1930s and compare the U.S. to Germany, for example. Even though Germany was far worse off than the U.S. during the depression, they were still the most advanced country in the world in terms of technology, science, music, etc.
It's no coincidence that the greatest advances in the U.S. during and after World War II were only possible (at that early time, at least) because the U.S. was able to tap Germany's knowledge base in nuclear science, aeronautics, and rocket propulsion research.