[Merged by Bors] - feat(Filter): lemmas from Mandelbrot connectedness project #7913
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- Add `Filter.frequently_iff_neBot` and `Filter.frequently_mem_iff_neBot`. - Drop some implicit arguments that are available from `variable`. - Add `Filter.disjoint_prod` and `Filter.frequently_prod_and`. - Swap `Filter.le_prod` with `Filter.tendsto_prod_iff'` to use the latter in the proof of the former.
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Thank you for doing this! And the golfing in |
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Oct 25, 2023
| @@ -1310,6 +1310,12 @@ theorem Eventually.exists {p : α → Prop} {f : Filter α} [NeBot f] (hp : ∀ | |||
| hp.frequently.exists | |||
| #align filter.eventually.exists Filter.Eventually.exists | |||
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| lemma frequently_iff_neBot {p : α → Prop} : (∃ᶠ x in l, p x) ↔ NeBot (l ⊓ 𝓟 {x | p x}) := by | |||
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Could you golf frequently_true_iff_neBot using this?
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- Add `Filter.frequently_iff_neBot` and `Filter.frequently_mem_iff_neBot`. - Drop some implicit arguments that are available from `variable`. - Add `Filter.disjoint_prod` and `Filter.frequently_prod_and`. - Swap `Filter.le_prod` with `Filter.tendsto_prod_iff'` to use the latter in the proof of the former. Co-Authored-By: @girving
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Add
Filter.frequently_iff_neBotand
Filter.frequently_mem_iff_neBot.Drop some implicit arguments
that are available from
variable.Add
Filter.disjoint_prodandFilter.frequently_prod_and.Swap
Filter.le_prodwithFilter.tendsto_prod_iff'to use the latter in the proof of the former.
Co-Authored-By: @girving