Betweenness+continued

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COMMENT: On Proposition 2.5 we didn't prove that the two sides are disjoint. My thinking is that we can prove this by contradiction. So, in this sense we'll prove that side(A, l) intersected with side(B, l) equals the empty set (when A and B are the two sides that we have previously shown exist). Say that there exists a point C that is an element of side(A, l) intersected with side(B, l). Then since C is an element of side(A,l) we know A and C are on the same side, but since C is an element of side(B,l) we know B and C are on the same side. That is a contradiction because of B-4 which states that in this case A, B, and C are all on the same side. So our sides must be disjoint, there is no point in the intersection of side(A, l) and side(B,l).

This still has not been improved. Where did A and C come from? What about B? **
 * Comment #2: Proposition 2.5 needs more work. Why? What are our assumptions? What is given? What needs to be shown?


 * **Yay! I'm glad it can be read! Thanks, Emina!** **