Giving a rigorous proof of the second theorem in a more general form that covers all such sentences, however, has turned out to be very complicated. The basic reason for this is that, unlike in the first theorem, not just any, merely extensionally adequate provability predicate works for the formalization of the consistency claim. The manner of presentation makes all the difference. For example, Rosser’s provability predicate mentioned above would not do; one can prove the “consistency” of \(F\)