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Formalization of the Fundamental Group in Untyped Set Theory Using Auto2

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Interactive Theorem Proving (ITP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10499))

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Abstract

We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group for an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.

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Notes

  1. 1.

    Code available at https://github.com/bzhan/auto2.

  2. 2.

    http://www.cs.nyu.edu/pipermail/fom/2014-October/018243.html.

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Acknowledgements

The author would like to thank the anonymous referees for their comments. This research is completed while the author is supported by NSF Award No. 1400713.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, USA

    Bohua Zhan

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  1. Bohua Zhan
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Correspondence to Bohua Zhan .

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Editors and Affiliations

  1. University of Brasília, Brasília D.F., Brazil

    Mauricio Ayala-Rincón

  2. NASA, Hampton, VA, USA

    César A. Muñoz

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Zhan, B. (2017). Formalization of the Fundamental Group in Untyped Set Theory Using Auto2. In: Ayala-Rincón, M., Muñoz, C.A. (eds) Interactive Theorem Proving. ITP 2017. Lecture Notes in Computer Science(), vol 10499. Springer, Cham. https://doi.org/10.1007/978-3-319-66107-0_32

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  • DOI: https://doi.org/10.1007/978-3-319-66107-0_32

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66106-3

  • Online ISBN: 978-3-319-66107-0

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