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A Mechanized Proof of Higman’s Lemma by Open Induction

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Well-Quasi Orders in Computation, Logic, Language and Reasoning

Part of the book series: Trends in Logic ((TREN,volume 53))

Abstract

I present a short, mechanically checked Isabelle/HOL formalization of Higman’s lemma by open induction.

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Notes

  1. 1.

    Dagstuhl Seminar 16031: www.dagstuhl.de/16031.

  2. 2.

    In fact, demanding transitivity suffices, since reflexivity is immediate for almost-full relations.

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Acknowledgements

I am grateful to Mizuhito Ogawa, who introduced me to open induction and the idea of applying it to formalize Higman’s lemma in the first place. Thanks goes also to the organizers and participants of the delightful Dagstuhl seminar on Well Quasi-Orders in Computer Science, for fruitful discussions and providing a nice atmosphere. I also want to thank Bertram Felgenhauer for giving me a nudge when I was stuck in the proof of Lemma 2(3).

Finally, I am indebted to an anonymous reviewer who pointed out many blemishes in my first draft and provided constructive (pun intended) criticism. Her or his feedback helped to improve this work and lead to a generalization (Lemma 4) of an earlier result (Corollary 2).

This work is supported by FWF (Austrian Science Fund) project P27502.

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Authors and Affiliations

  1. University of Innsbruck, Technikerstraße 21a, 6020, Innsbruck, Austria

    Christian Sternagel

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  1. Christian Sternagel
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Correspondence to Christian Sternagel .

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  1. Dipartimento di Informatica, Università degli Studi di Verona, Verona, Italy

    Peter M. Schuster

  2. Department of Computer Science, Swansea University, Swansea, UK

    Monika Seisenberger

  3. Vakgroep Wiskunde, Ghent University, Ghent, Belgium

    Andreas Weiermann

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Sternagel, C. (2020). A Mechanized Proof of Higman’s Lemma by Open Induction. In: Schuster, P., Seisenberger, M., Weiermann, A. (eds) Well-Quasi Orders in Computation, Logic, Language and Reasoning. Trends in Logic, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-30229-0_12

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