Starting towards a proof that one region defined by a polygon is unbounded.

Theorem that the line of a half plane lies on a plane. Seems important.
Another theorem to obtain the other half plane given a half plane. Might not be so important.
Got rid of the theorem to obtain other half-plane. Seemed too easy to prove and don't think I need it.
Another theorem to show that a point is neither in a half-plane nor on the line of the half-plane based on a betweeness assumption.
Case-splitting on whether ys in x:ys is empty. I don't think this is the right way to go. We probably want to case split on the size of IMAGE g.
Case when the image of f is a singleton.
Got required half-plane. Just need to show that all points lie in this half-plane.