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### Abstract

This article is a formalisation of a proof of the
Hales–Jewett theorem presented in the textbook *Ramsey
Theory* by Graham et al.

The Hales–Jewett theorem is a result in Ramsey Theory which states that, for any non-negative integers $r$ and $t$, there exists a minimal dimension $N$, such that any $r$-coloured $N'$-dimensional cube over $t$ elements (with $N' \geq N$) contains a monochromatic line. This theorem generalises Van der Waerden's Theorem, which has already been formalised in another AFP entry.