Picard–Lindelöf theorem

Hey, can someone explain to me how the Picard–Lindelöf theorem proves the existence and uniqueness of initial value problems?

That is exactly the theorem.

If you don't understand the proof, I can't really be bothered to help you, but not to understand how the theorem proves the conclusion of the theorem, that's a new depth of stupidity really.

Well okay, I'm really stupid. Can you help me with the proof then?

>>3
Look at your notes.

http://en.wikipedia.org/wiki/Picard-Lindel%C3%B6f_theorem

There's a proof in the external links.