can be stated as follows:

The proof can be outlined as follows. Suppose we first try to find a quantization map on polynomials of degree less than or equal to three satisfying the bracket condition whenever has degree less than or equal to two and has degree less than or equal to two. Then there is precisely one such map, and it is the Weyl quantization. The impossibility result now is obtained by writing the same polynomial of degree four as a Poisson bracket of polynomials of degree three