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Readable Formalization of Euler’s Partition Theorem in Mizar

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Intelligent Computer Mathematics (CICM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9150))

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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.

The paper has been financed by the resources of the Polish National Science Center granted by decision n\(^{\circ }\)DEC-2012/07/N/ST6/02147.

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Notes

  1. 1.

    For more details see https://code.google.com/p/hol-light/source/browse/trunk/100/euler.ml?r=2.

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Authors and Affiliations

  1. Institute of Informatics, University of Bialystok, Bialystok, Poland

    Karol Pąk

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  1. Karol Pąk
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Correspondence to Karol Pąk .

Editor information

Editors and Affiliations

  1. School of Computer Science, University of Birmingham, Birmingham, United Kingdom

    Manfred Kerber

  2. McMaster University, Hamilton, Ontario, Canada

    Jacques Carette

  3. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  4. Jacobs University Bremen, Bremen, Germany

    Florian Rabe

  5. University of Birmingham, Birmingham, United Kingdom

    Volker Sorge

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Pąk, K. (2015). Readable Formalization of Euler’s Partition Theorem in Mizar. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds) Intelligent Computer Mathematics. CICM 2015. Lecture Notes in Computer Science(), vol 9150. Springer, Cham. https://doi.org/10.1007/978-3-319-20615-8_14

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  • DOI: https://doi.org/10.1007/978-3-319-20615-8_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20614-1

  • Online ISBN: 978-3-319-20615-8

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