Part on "Proof Methods"

[rzach]

We need a part that covers methods of proof, including inductive definitions and inductive proofs.

[rzach]

In progress: see "methods" branch.

[rzach]

One issue: https://github.com/OpenLogicProject/OpenLogic/blob/master/content/sets-functions-relations/sets/proofs-about-sets.tex is a very short intro on how to prove things about sets. A whole chapter on proving things about sets supercedes this. Take it out? Make it shorter with a reference to the chapter? Leave it in (but don't include it in Sets, Logic, Computation)?

[rzach]

Started a branch proofs, see bb92fa3

[rzach]

Needs: proving from existence claims, indirect proof, and what to leave out when writing it down, what to interpolate when reading a proof. Also, exercises. And deciding what to do with the one section in SFR/sets that deals with proofs about sets.

[nicolewyatt]

Would it be possible to remove https://github.com/OpenLogicProject/OpenLogic/blob/master/content/sets-functions-relations/sets/proofs-about-sets.tex from the sets-functions-relations default once the chapter on proving things about sets is complete, but maybe keep it somewhere as an option, for people who don't want the whole chapter on proofs?

[rzach]

Yes, re: "deciding what to do with the one section in SFR/sets that deals with proofs about sets."

1. We leave the section in the main text but remove it from SLC as is.
2. We shorten it and keep it as an example in the main text, including in SLC.
3. We move it to the methods/proofs chapter as a third example.

[rzach]

Ok, this is now reasonably complete:
http://people.ucalgary.ca/~rzach/static/open-logic/branches/proofs/open-logic-complete.pdf#chapter.29
Do we need (more) examples? Exercises?
And, what do we do about the proofs-about-sets section?

[rzach]

Done (49e50f3)

Samara proofread it. I removed the proofs-about-sets section from the chapter but left the file in place. I used the material for the reading-proofs section.