[Merged by Bors] - feat: stationary sets

[vihdzp]

We define stationary sets as sets intersecting all club sets, and prove basic theorems about them.

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[github-actions]

PR summary 69a36e5635

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ IsClub.isStationary
+ IsCofinal.nonempty
+ IsStationary
+ IsStationary.mono
+ IsStationary.nonempty
+ IsStationary.of_not_isCofinal_compl
+ IsStationary.univ
+ _root_.isClub_empty_iff
+ iInter_of_countable
+ isStationary_iUnion_iff
+ isStationary_iUnion_iff_of_cof_le_one
+ isStationary_iUnion_iff_of_countable
+ isStationary_iUnion_iff_of_orderTop
+ isStationary_sUnion_iff
+ isStationary_sUnion_iff_of_cof_le_one
+ isStationary_sUnion_iff_of_countable
+ isStationary_sUnion_iff_of_orderTop
+ isStationary_union_iff
+ isStationary_univ_iff
+ nonempty
+ not_isStationary_empty
+ not_isStationary_iff
+ not_isStationary_of_isEmpty
+ sInter_of_countable

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 69a36e5).

• +24 new declarations
• −0 removed declarations

+IsClub.iInter_of_countable
+IsClub.isStationary
+IsClub.nonempty
+IsClub.sInter_of_countable
+IsCofinal.nonempty
+IsStationary
+IsStationary.mono
+IsStationary.nonempty
+IsStationary.of_not_isCofinal_compl
+IsStationary.univ
+isClub_empty_iff
+isStationary_iUnion_iff
+isStationary_iUnion_iff_of_cof_le_one
+isStationary_iUnion_iff_of_countable
+isStationary_iUnion_iff_of_orderTop
+isStationary_sUnion_iff
+isStationary_sUnion_iff_of_cof_le_one
+isStationary_sUnion_iff_of_countable
+isStationary_sUnion_iff_of_orderTop
+isStationary_union_iff
+isStationary_univ_iff
+not_isStationary_empty
+not_isStationary_iff
+not_isStationary_of_isEmpty

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 69a36e5635
Reference commit 7516f8d024

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[YaelDillies]

Maybe add not_isStationary_of_isEmpty as a simp lemma?

[YaelDillies]

Thanks! 🚀

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by YaelDillies.

[b-mehta]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Lint style
• ci (staging) / Post-Build Step
• ci (staging) / Build
• ci (staging) / Post-CI job