Understanding Post's Theorem in Propositional Calculus

[Goldenwind]

Can someone explain to me what the heck Post's Theorem is? Every time my professor does something that seems to make absolutely no sense, he sites his method as "Post". I've compared the various times he uses Post, and there seems to be no pattern. I'm beginning to think that he just uses it to excuse something he wants to make it (I know this isn't true, but seems like it).

I've tried looking it up. Both the textbook and wikipedia just give a tonne more symbols that I don't understand.

Cut rule, for example, is simple: |- A -> B becomes A |- B
Can someone lay out Post simply like that? :(

 

[Goldenwind]

'kay. This is all in studying for my exam, which is in about 17 hours, so I'll be a bit more specific.

http://www.cse.yorku.ca/~gt/courses/MATH1090F07/asg4-sol.pdf

The first problem that is shown uses Post to demonstrate that if you have A -> (B=C) and A -> B, then A -> C due to the fact that B and C must have the same value. I understand this. Is this rule called "Post"? Maybe. Take a look in future questions.

The second problem uses "Post" to demonstrate that (A v B) -> C is the same thing as A -> C. Not only does this not make sense to me, it also seems to have nothing to do with the "Post" theorem that we used in the first problem. Why is this true, and what does the "Post" theorem really mean?