The problem:

$\displaystyle L$ a Lie algebra. Let $\displaystyle H \lhd L$ and $\displaystyle K \leq L$. Then prove that $\displaystyle H+K := \{ h+k : h \in H, k \in K\}$ is a subalgebra of $\displaystyle L$.

Never mind - I was attempting to show it was an ideal, not a subalgebra. Is it possible to delete posts?