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An Intuitionistic Proof of a Discrete Form of the Jordan Curve Theorem Formalized in Coq with Combinatorial Hypermaps

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Abstract

This paper presents a completely formalized proof of a discrete form of the Jordan Curve Theorem. It is based on a hypermap model of planar subdivisions, formal specifications and proofs assisted by the Coq system. Fundamental properties are proven by structural or noetherian induction: Genus Theorem, Euler Formula, constructive planarity criteria. A notion of ring of faces is inductively defined and a Jordan Curve Theorem is stated and proven for any planar hypermap.

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Authors and Affiliations

  1. UFR de Mathématique et d’Informatique, Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection (UMR CNRS-ULP 7005), Université de Strasbourg, Pôle API, Boulevard Sébastien Brant, 67400, Illkirch, France

    Jean-François Dufourd

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  1. Jean-François Dufourd
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Correspondence to Jean-François Dufourd.

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This research is supported by the “white” project GALAPAGOS, French ANR, 2007.

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Dufourd, JF. An Intuitionistic Proof of a Discrete Form of the Jordan Curve Theorem Formalized in Coq with Combinatorial Hypermaps. J Autom Reasoning 43, 19–51 (2009). https://doi.org/10.1007/s10817-009-9117-x

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