Weyl's Theorem states that if $L$ is a semisimple Lie algebra over $\mathbb{C}$, then any finite dimensional representation of $L$ is completely reducible.
I want to show that a corollary of this is that if $L$ is a semisimple Lie algebra over $\mathbb{C}$, then we are able to decompose $L$ into a direct sum of simple ideals, say $L=L_1\oplus \dots \oplus L_s$, where $L_i$ are simple ideals.
Weyls' Theorem tells us that if we have $(\rho, V)$ as a (finite dimensional) representation for $L$, then we can write $V=V_1 \oplus \dots \oplus V_r$, a direct sum of irreducible subrepresentations, where each $V_i$ is $L$ - stable.
I'm not sure where to proceed from here, I would appreciate any suggestions.