### 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.

### License

BSD License

### Topics

- Mathematics/Combinatorics

### Session Hales_Jewett

- Hales_Jewett

## Cite

×

Hales_Jewett-AFP

    @article{Hales_Jewett-AFP,
      author  = {Ujkan Sulejmani and Manuel Eberl and Katharina Kreuzer},
      title   = {The Hales–Jewett Theorem},
      journal = {Archive of Formal Proofs},
      month   = {September},
      year    = {2022},
      note    = {\url{https://isa-afp.org/entries/Hales_Jewett.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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