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My problem is not applying it, but understanding exactly how the steps I am taking prove whatever it is I am doing. I can apply it and prove things with it, but I would really like to know exactly what it is I am doing in proving a base case, assuming for n, and then proving for n+1.

Thanks in advance for answer to this question. I know it is kind of basic, but it didn't really fit the format for the Homework subforum.