feat: Fodor's lemma

[vihdzp]

We define stationary sets and prove Fodor's lemma, following the proof at Wikipedia.

---

• depends on: [Merged by Bors] - feat: stationary sets #39727

I'm surprised that this has a Wikipedia article but isn't listed in 1000.yaml. Is it just because the name has "lemma" instead of "theorem"?

[github-actions]

PR summary 8319de3ea3

Import changes exceeding 2%

%	File
+7.33%	Mathlib.SetTheory.Cardinal.Cofinality.Club

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.SetTheory.Cardinal.Cofinality.Club	696	747	+51 (+7.33%)

Import changes for all files

Files	Import difference
Mathlib.SetTheory.Cardinal.Cofinality.Club	51

---

Declarations diff (regex)

+ ciSup_mem
+ diag
+ exists_isStationary_preimage_singleton

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 8319de3).

• +3 new declarations
• −0 removed declarations

+IsClub.ciSup_mem
+IsClub.diag
+exists_isStationary_preimage_singleton

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 8319de3ea3
Reference commit 914b89d98d

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).

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat: stationary sets #39727
  By Dependent Issues (🤖). Happy coding!

[YaelDillies]

What's diagonal about this? Mayve worth giving the lemma a more syntactic name?

[staroperator]

It's called diagonal intersection in Kunen's book (page 220).

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.