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feat(measure_theory/function/intersectivity): Bergelson Intersectivity Lemma #18732
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| refine ⟨{n | x ∈ s n}, λ hxs, _, λ u hux hu, _⟩, | ||
| -- This next block proves that a set of strictly positive natural density is infinite, mixed with | ||
| -- the fact that `{n | x ∈ s n}` has strictly positive natural density. | ||
| -- TODO: Separate it out to a lemma once we have a natural density API. |
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IMHO, you should separate it to a lemma now, then migrate to a new API when it's available.
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Eh I'm not sure how to go about this. There's some plumbing involved and figuring it out is probably as hard as writing the density API in the first place. The density API is on my todo list, so I'm definitely not forgetting that todo.
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Wait, why is this marked |
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Prove a weak version of the Bergelson intersectivity lemma. The proof gives the strong version, but we need natural density to state it. This is a prerequisite to Tao and Ziegler's recent paper Infinite partial sumsets in the primes.