 
Summary: 1
A computerchecked proof of the Four Colour Theorem
Georges Gonthier
Microsoft Research Cambridge
This report gives an account of a successful formalization of the proof of the Four
Colour 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.
1 The story
The Four Colour Theorem is famous for being the first longstanding mathematical
problem to be resolved using a computer program. The theorem was first conjectured
in 1852 by Francis Guthrie, and after over a century of work by many famous
