Mizar Set Comprehension in Isabelle Framework

Abstract

The Mizar project from its beginning aimed to make a highly human oriented proof environment where the proof style closely reflects the informal proofs style. The support is reflected in the size of the largest consistent formal library -Mizar Mathematical Library (MML). However, the Mizar system is the only tool that provides full verification and further development of the MML. In this paper, we present the progress in the development of the Isabelle/Mizar project whose main goal is independent cross-verification of the MML in Isabelle. We focus on Mizar set comprehension operators that allow defining sets that satisfy a given predicate. The development already covers simple cases where the arity of predicates is limited to two. We propose an infrastructure that provides a more elegant and recursive approach to construct and to provide the main property of set comprehension operators.