It can be hard to prove logical statements. When the statement we are trying to prove is to bound the difficulty of another problem, the complexity of the proof is the derivative* of the complexity of the other problem's complexity. When I first thought of this relationship, many years ago, I thought that it was an interesting curiosity and maybe coincidence. It seems that complexity has to work this way. That is to say that it cannot be disproven, which is what is important here (consistency over provability <- incompletness). This is a very important investigative tool for open problems. It is a way to test for logical incompleteness. 

* Yes, I know that f(x+1) - f(x) is not a derivative. In general, discrete spaces do not have a metric. We can choose to think of f(x+1) - f(x) as a generalization of a derivative for the sake of computations. It does not really matter what we call it. Just thought it would grab your attention. It could provoke you to rethink computation and complexity. shucks