Let $\delta$ be a derivation of a complex Lie algebra L, and for $\lambda \in C$, let $$L_{\lambda}=\lbrace x \in L:(\delta-\lambda 1_{L})^{m}\;x=0 \mbox{ for some } m \ge 1 \rbrace$$

be the generalised eigenspace of $\delta$ corresponding to $\lambda$.

Why $[L_{\lambda},L_{\mu}] \subseteq L_{\lambda+\mu}$?