In 'Infinite Dimensional Lie Algebras, 3rd edition', Kac mentions at the top of p. 170 that 'a simple cohomological proof of Theorem 9.11 was found by O. Mathieu (unpublished)'.

Does anyone know how this proof goes?

For reference, 9.11 is the statement that given a symmetrizable generalized Cartan matrix $A$, with associated lie algebra $\tilde{\mathfrak{g}}(A)$ with only the Weyl relations, the maximal ideal not intersecting $\mathfrak{h}$ is generated by the Serre relations. Thank you in advance.