Pascal’s Theorem in Real Projective Plane

Pole DC	Wartość	Język
dc.contributor.author	Coghetto, Roland	-
dc.date.accessioned	2018-02-08T08:10:29Z	-
dc.date.available	2018-02-08T08:10:29Z	-
dc.date.issued	2017	-
dc.identifier.citation	Formalized Mathematics, Volume 25, Issue 2, Pages 107–119	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/6279	-
dc.description.abstract	SummaryIn this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines. For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s work. With HOL Light, he has the proof of Pascal’s theorem2. For a lemma, we use PROVER93 and OTT2MIZ by Josef Urban4 [12, 6, 7]. We note, that we don’t use Skolem/Herbrand functions (see “Skolemization” in [1]).	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	Pascal’s theorem	-
dc.subject	real projective plane	-
dc.subject	Grassman-Plücker relation	-
dc.title	Pascal’s Theorem in Real Projective Plane	-
dc.type	Article	-
dc.identifier.doi	10.1515/forma-2017-0011	-
dc.description.Affiliation	Rue de la Brasserie 5, 7100 La Louvière, Belgium	-
dc.description.references	Jesse Alama. Escape to Mizar for ATPs. arXiv preprint arXiv:1204.6615, 2012.	-
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007/978-3-319-20615-817.	-
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dc.description.references	Piotr Rudnicki and Josef Urban. Escape to ATP for Mizar. In First International Workshop on Proof eXchange for Theorem Proving-PxTP 2011, 2011.	-
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dc.identifier.eissn	1898-9934	-
dc.description.volume	25	-
dc.description.issue	2	-
dc.description.firstpage	107	-
dc.description.lastpage	119	-
dc.identifier.citation2	Formalized Mathematics	-
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