Readable Formalization of Euler’s Partition Theorem in Mizar

Abstract

We present a case study on formalization of a textbook theorem in a form that is as close to the original textbook presentation as possible. Euler's partition theorem, listed as #45 at Freek Wiedijk's list of Top 100 mathematical theorems, is taken as the subject of the study. As a result new formal concepts including informal flexary i.e. flexible arity addition are created and existing ones are extended to go around existing limitations of the Mizar system, without modification of its core. Such developments bring more flexibility of informal language reasoning into the Mizar system and make it useful for wider audience.