[Merged by Bors] - feat: monotone function Cardinal → α is eventually constant

[vihdzp]

---

• depends on: [Merged by Bors] - feat: rangeSplitting f is strictly monotone when f is monotone #39797

[github-actions]

PR summary e0aaae81da

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.SetTheory.Cardinal.EventuallyConst (new file)	771

---

Declarations diff (regex)

+ Antitone.isChain_image
+ Antitone.isChain_range
+ IsChain.linearOrder
+ of_antitone_of_lt_cof
+ of_monotone_of_lt_cof
+ of_not_isCofinal_rangeSplitting
+ small_orderDual
++ eventuallyConst_of_antitone
++ eventuallyConst_of_monotone

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 e0aaae8).

• +11 new declarations
• −0 removed declarations

+Antitone.isChain_image
+Antitone.isChain_range
+Cardinal.eventuallyConst_of_antitone
+Cardinal.eventuallyConst_of_monotone
+Filter.EventuallyConst.of_antitone_of_lt_cof
+Filter.EventuallyConst.of_monotone_of_lt_cof
+Filter.EventuallyConst.of_not_isCofinal_rangeSplitting
+IsChain.linearOrder
+Ordinal.eventuallyConst_of_antitone
+Ordinal.eventuallyConst_of_monotone
+small_orderDual

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit e0aaae81da
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]

Doesn't this generalise to maps α → β where α is a non-small linear order and β is a small preorder?

[vihdzp]

This actually generalizes to maps α → β where #β < cof α. I'll prove this generalization shortly.

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat: rangeSplitting f is strictly monotone when f is monotone #39797
  By Dependent Issues (🤖). Happy coding!

[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