feat(Topology/Order): add nonempty_nhds_inter_Ioi#37550
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pitmonticone wants to merge 2 commits intoleanprover-community:masterfrom
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feat(Topology/Order): add nonempty_nhds_inter_Ioi#37550pitmonticone wants to merge 2 commits intoleanprover-community:masterfrom
nonempty_nhds_inter_Ioi#37550pitmonticone wants to merge 2 commits intoleanprover-community:masterfrom
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PR summary caa79c2e3cImport changes for modified filesNo significant changes to the import graph Import changes for all files
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| theorem nonempty_nhds_inter_Ioi [DenselyOrdered α] {x : α} {u : Set α} | ||
| (hu : u ∈ nhds x) (hx : ¬ IsMax x) : | ||
| (u ∩ Set.Ioi x).Nonempty := by | ||
| obtain ⟨b, hx⟩ := not_isMax_iff.mp hx | ||
| obtain ⟨b, hb, Ico_sub⟩ := exists_Ico_subset_of_mem_nhds' hu hx | ||
| obtain ⟨a, x_lt_a, a_lt_b⟩ := exists_between hb.1 | ||
| exact ⟨a, Ico_sub ⟨x_lt_a.le, a_lt_b⟩, x_lt_a⟩ |
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I'm not sure I'm a big fan of adding this, is it too annoying to use closure_Ioi' together with mem_closure_iff_nhds?
In any case, if we really want this :
- This should go in
Mathlib.Topology.Order.DenselyOrdered - This should be proven using the two lemmas I just mentioned
- There should be similar lemmas for other type of intervals
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Ok, thanks! Moved to DenselyOrdered, reproved via |
…s_inter_Iio` Add `nonempty_nhds_inter_Ioi` and `nonempty_nhds_inter_Iio`: a neighborhood of `x` has nonempty intersection with `Ioi x` (resp. `Iio x`) when `x` is not a maximum (resp. minimum). Upstreamed from the [Carleson](https://github.com/fpvandoorn/carleson) project. Co-authored-by: Leo Diedering <[email protected]> Co-authored-by: Michael Rothgang <[email protected]>
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nonempty_nhds_inter_Ioi: a neighborhood ofxhas nonempty intersection withIoi xwhenxis not a maximum.Upstreamed from the Carleson project.
Co-authored-by: Leo Diedering [email protected]
Co-authored-by: Michael Rothgang [email protected]