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monoAP_guarantee_set_nonempty

Specification

Asserts that for any number of colors `r` and any progression length `k`, there always exists some number `N` large enough to guarantee a monochromatic arithmetic progression. In other words, the set `monoAP_guarantee_set` is non-empty. This is the fundamental existence result that allows for the definition of the van der Waerden numbers.

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Lean 4 Statement
theorem monoAP_guarantee_set_nonempty (r k) : (monoAP_guarantee_set r k).Nonempty
ID: ErdosProblems__138__monoAP_guarantee_set_nonempty
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