https://hal.inria.fr/hal-04034866Gonthier, GeorgesGeorgesGonthierMicrosoft - Microsoft Research [Cambridge] - Microsoft ResearchA computer-checked proof of the Four Color TheoremHAL CCSD2023[INFO] Computer Science [cs][MATH] Mathematics [math]Mahboubi, Assia2023-03-17 16:06:382023-03-18 03:34:372023-03-17 17:03:53enReportsapplication/pdf1This 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.