Formalization of the Fundamental Group in Untyped Set Theory Using Auto2

摘要

We present a new framework for formalizing mathematics in untyped set theory using auto2. We demonstrate that many difficulties with using set theory for formalization of mathematics can be addressed by improvements to automation, without sacrificing the inherent flexibility of the logic. As applications, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group of an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.