feat(topology/algebra/infinite_sum): dot notation, cauchy sequences #2171
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sgouezel
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| lemma tsum_eq_has_sum (ha : has_sum f a) : (∑b, f b) = a := has_sum_unique (has_sum_tsum ⟨a, ha⟩) ha | ||
| lemma tsum_eq_has_sum (ha : has_sum f a) : (∑b, f b) = a := | ||
| has_sum_unique (summable.has_sum ⟨a, ha⟩) ha | ||
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| lemma has_sum_iff_of_summable (h : summable f) : has_sum f a ↔ (∑b, f b) = a := |
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This has prompted me to check the file again, and I have found two or three other lemmas that could benefit from the dot notation. Done.
urkud
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A few minor comments, otherwise LGTM. |
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Thanks for your comments! |
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…2171) * more material on infinite sums * minor fixes * cleanup * yury's comments Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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…eanprover-community#2171) * more material on infinite sums * minor fixes * cleanup * yury's comments Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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…eanprover-community#2171) * more material on infinite sums * minor fixes * cleanup * yury's comments Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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Cleanup of the file
infinite_sum.lean, adding what I will need to define analytic functions in a later PR. Two main things:has_sum.add,has_sum.summable,summable.has_sumand so on)s -> s.sum fis a Cauchy sequence when the finsetstends toat_top.Plus many minor missing lemmas scattered all over the place.