tensor product of finite-dimensional irreducible modules for a semisimple Lie algebra

Question

How to prove the following statement:

If $g$ is a semisimple Lie algebra, then the tensor product of finite-dimensional irreducible modules possesses the crucial property of being fully reducible.

Answer 1

If $\mathfrak{g}$ is semisimple then all of its finite-dimensional modules are completely reducible (in characteristic zero) --- that's Weyl's theorem