This library contains a formal proof of the Four Color Theorem in Coq, along with the theories needed to support stating and then proving the Theorem. This includes an axiomatization of the setoid of classical real numbers, basic plane topology definitions, and a theory of combinatorial hypermaps.

• Author(s):
  • Georges Gonthier (initial)
• Coq-community maintainer(s):
  • Yves Bertot (@ybertot)
• License: CeCILL-B
• Compatible Coq versions: 8.16 or later
• Additional dependencies:
  • MathComp ssreflect 2.1.0 or later
  • MathComp algebra
  • Hierarchy Builder 1.5.0 or later
• Coq namespace: fourcolor
• Related publication(s):
  • Formal Proof—The Four-Color Theorem
  • A computer-checked proof of the Four Color Theorem

The easiest way to install the latest released version of The Four Color Theorem is via OPAM:

opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-fourcolor

To instead build and install manually, do:

git clone https://github.com/coq-community/fourcolor.git
cd fourcolor
make   # or make -j <number-of-cores-on-your-machine> 
make install

The Four Color Theorem (Appel & Haken, 1976) is a landmark result of graph theory.

The formal proof is based on the Mathematical Components library.