Proof. Indeed, for the monomial $R_{\alpha_{1}}^{-n_{1}}R_{\alpha_{2}}^{-n_{2}}\in{\bf g}_{\lambda}$ which maps non-trivially to the quotient ${\bf g}_{\lambda}/{\bf g}^{\geq k}_{\lambda}$ we have: $n_{1}+n_{2}\leq k,n_{1}/n_{2}=\lambda$, where $n_{1},n_{2}$ are non-negative integers. There are finitely many such non-negative integers $n_{1}$ and $n_{2}$. $\blacksquare$