Spinoza's Ethics, book 2 Of the Mind, Proposition 13?

Can anyone please explain what he's saying in plain english? if you're going to write me a one liner explanation you're wasting your time. there's 7 lemas and a corollary that need explaining. Thus far I gather he is talking about the unison of the mind and body in man, and begins explaining the nature of how bodies interact, then provides proofs. If I'm off, please throw that in your answer as well. thank you!