and we color "A" with two colors, then "A" contains at least one arithmetic progression of length three, all of whose elements are the same color. This is simply because all of the combinatorial lines appearing in the above proof of the Hales–Jewett theorem, also form arithmetic progressions in decimal notation. A more general formulation of this argument can be used to show that the Hales–Jewett theorem generalizes van der Waerden's theorem. Indeed the Hales–Jewett theorem is substantially a stronger theorem.