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Rapport Année : 2023

A computer-checked proof of the Four Color Theorem


This report gives an account of a successful formalization of the proof of the Four Color Theorem, which was fully checked by the Coq v7.3.1 proof assistant [13]. This proof is largely based on the mixed mathematics/computer proof [26] of Robertson et al., but contains original contributions as well. This document is organized as follows: section 1 gives a historical introduction to the problem and positions our work in this setting; section 2 defines more precisely what was proved; section 3 explains the broad outline of the proof; section 4 explains how we exploited the features of the Coq assistant to conduct the proof, and gives a brief description of the tactic shell that we used to write our proof scripts; section 5 is a detailed account of the formal proof (for even more details the actual scripts can be consulted); section 6 is a chronological account of how the formal proof was developed; finally, we draw some general conclusions in section 7.
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Dates et versions

hal-04034866 , version 1 (17-03-2023)


  • HAL Id : hal-04034866 , version 1


Georges Gonthier. A computer-checked proof of the Four Color Theorem. Inria. 2023. ⟨hal-04034866⟩


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