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Formalizing Projective Plane Geometry in Coq

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Automated Deduction in Geometry (ADG 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6301))

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Abstract

We investigate how projective plane geometry can be formalized in a proof assistant such as Coq. Such a formalization increases the reliability of textbook proofs whose details and particular cases are often overlooked and left to the reader as exercises. Projective plane geometry is described through two different axiom systems which are formally proved equivalent. Usual properties such as decidability of equality of points (and lines) are then proved in a constructive way. The duality principle as well as formal models of projective plane geometry are then studied and implemented in Coq. Finally, we formally prove in Coq that Desargues’ property is independent of the axioms of projective plane geometry.

This work is partially supported by the ANR project Galapagos.

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Magaud, N., Narboux, J., Schreck, P. (2011). Formalizing Projective Plane Geometry in Coq. In: Sturm, T., Zengler, C. (eds) Automated Deduction in Geometry. ADG 2008. Lecture Notes in Computer Science(), vol 6301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21046-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-21046-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21045-7

  • Online ISBN: 978-3-642-21046-4

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