User blog:KthulhuHimself/I'm trying to (or could use some help) prove something interesting.

Well, I'll try to put this in the simplest terms (even though it's pretty simple either way).

(I know this is basically the Godel's-incompleteness-theorem thing, but we'll go on with it anyways.)

The thing
Let P be some formal system in which there are no contradictions between the axioms, and A be some axiom.

PA(AP)

It almost seems trivial; but I'd stil like some nice formal proof.

The statements on the sides
We should also say that

P P' ( (P ' P))

But, well; I guess it's up for debate whether or not this is even necessary.

The consequence
(We'll get to this once the previous are proven.)