What PA does not prove is that the largest consistent subset of PA is, in fact, the whole of PA. (The term "largest consistent subset of PA" is meant here to be the largest consistent initial segment of the axioms of PA under some particular effective enumeration.) The standard proof of the second incompleteness theorem assumes that the provability predicate ProvA("P") satisfies the Hilbert–Bernays provability conditions. Letting #("P") represent the Gödel number of a formula "P", the derivability conditions say:   There are systems, such as Robinson arithmetic, which are strong enough to meet the assumptions of the first incompleteness theorem, but which do not prove the Hilbert—Bernays conditions. Peano arithmetic, however, is strong enough to verify these conditions, as are all theories stronger than Peano arithmetic. Gödel's second incompleteness theorem also implies that a system "F"1 satisfying the technical conditions outlined above cannot prove the consistency of any system "F"2 that proves the consistency of "F"1. This is because such a system "F"1 can prove that if "F"2 proves the consistency of "F"1, then "F"1 is in fact consistent. For the claim that "F"1 is consistent has form "for all numbers "n", "n" has the decidable property of not being a code for a proof of contradiction in "F"1". If "F"1 were in fact inconsistent, then "F"2 would prove for some "n" that "n" is the code of a contradiction in "F"1. But if "F"2 also proved that "F"1 is consistent (that is, that there is no such "n"), then it would itself be inconsistent. This reasoning can be formalized in "F"1 to show that if "F"2 is consistent, then "F"1 is consistent. Since, by second incompleteness theorem, "F"1 does not prove its consistency, it cannot prove the consistency of "F"2 either. This corollary of the second incompleteness theorem shows that there is no hope of proving, for example, the consistency of Peano arithmetic using any finitistic means that can be formalized in a system the consistency of which is provable in Peano arithmetic (PA). For example, the system of primitive recursive arithmetic (PRA), which is widely accepted as an accurate formalization of finitistic mathematics, is provably consistent in PA.