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Mizar system information


Mizar
Screenshot
Mizar MathWiki screenshot
ParadigmDeclarative
Designed byAndrzej Trybulec
First appeared1973
Typing disciplineWeak, static
Filename extensions.miz .voc
Websitewww.mizar.org
Influenced by
Automath
Influenced
OMDoc, HOL Light and Coq mizar modes

The Mizar system consists of a formal language for writing mathematical definitions and proofs, a proof assistant, which is able to mechanically check proofs written in this language, and a library of formalized mathematics, which can be used in the proof of new theorems.[1] The system is maintained and developed by the Mizar Project, formerly under the direction of its founder Andrzej Trybulec.

In 2009 the Mizar Mathematical Library was the largest coherent body of strictly formalized mathematics in existence.[2]

  1. ^ Naumowicz, Adam; Artur Korniłowicz (2009). A Brief Overview of Mizar. Lecture Notes in Computer Science. Vol. 5674. pp. 67–72. doi:10.1007/978-3-642-03359-9_5. ISBN 978-3-642-03358-2. {{cite book}}: |journal= ignored (help)
  2. ^ Wiedijk, Freek (2009). "Formalizing Arrow's theorem". Sādhanā. 34 (1): 193–220. doi:10.1007/s12046-009-0005-1. hdl:2066/75428.

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companion of Mizar. Mizar, also designated Zeta Ursae Majoris (ζ Ursae Majoris, abbreviated Zeta UMa, ζ UMa), is itself a quadruple system and Alcor, also...

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the Mizar system, the system can be considered a sextuple. Jabbah AR Cassiopeiae V871 Centauri Gamma Cassiopeiae QZ Carinae Exoplanet Solar System The...

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Borel set

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Mathematics, EMS Press, 2001 [1994] Formal definition of Borel Sets in the Mizar system, and the list of theorems Archived 2020-06-01 at the Wayback Machine...

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Probability axioms

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Probability Theory. New York: Macmillan. pp. 13–28. Formal definition of probability in the Mizar system, and the list of theorems formally proved about it....

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Intermediate value theorem

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"Two-dimensional version of the Intermediate Value Theorem". Stack Exchange. Mizar system proof: http://mizar.org/version/current/html/topreal5.html#T4...

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Double star

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naked eye is the case of Mizar and Alcor (though actually a multiple-star system), but it is not known for certain whether Mizar and Alcor are gravitationally...

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Steinitz exchange lemma

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Field extensions and Galois Theory, Addison–Wesley Publishing Company (1984). Mizar system proof: http://mizar.org/version/current/html/vectsp_9.html#T19...

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Extreme value theorem

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Demonstrations Project. Weisstein, Eric W. "Extreme Value Theorem". MathWorld. Mizar system proof: http://mizar.org/version/current/html/weierstr.html#T15...

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Tietze extension theorem

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Weisstein, Eric W. "Tietze's Extension Theorem." From MathWorld Mizar system proof: http://mizar.org/version/current/html/tietze.html#T23 Bonan, Edmond (1971)...

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USNS Mizar

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USNS Mizar (MA-48/T-AGOR-11/T-AK-272) was a vessel of the United States Navy. She was named after the star Mizar. Mizar was built as a small ice-strengthened...

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Fundamental theorem of algebra

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(in Latin) at Google Books Gauss's first proof (in Latin) at Google Books Mizar system proof: http://mizar.org/version/current/html/polynom5.html#T74...

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Yoneda lemma

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Press, 17 June 2010, ISBN 978-0-19-958736-0 Yoneda lemma at the nLab Mizar system proof: Wojciechowski, M. (1997). "Yoneda Embedding". Formalized Mathematics...

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Jordan curve theorem

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in 2005 by an international team of mathematicians using the Mizar system. Both the Mizar and the HOL Light proof rely on libraries of previously proved...

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