[NoneMore]

Add an equivalence between a direct limit and its component at an upper-bound index. Use it to prove upper and lower cardinality bounds and criteria for computing the cardinality of direct limits.

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AI disclosure: Most declarations, comments, and documentation in this PR were generated with Codex.

[github-actions]

PR summary 12137923ca

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.SetTheory.Cardinal.DirectLimit (new file)	909

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Declarations diff (regex)

+ equivOfIsTop
+ mk_eq_iSup_lift_mk
+ mk_eq_of_forall_lift_mk_eq
+ mk_le_of_aleph0_le
+ mk_le_sum

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 1213792).

• +5 new declarations
• −0 removed declarations

+DirectLimit.equivOfIsTop
+DirectLimit.mk_eq_iSup_lift_mk
+DirectLimit.mk_eq_of_forall_lift_mk_eq
+DirectLimit.mk_le_of_aleph0_le
+DirectLimit.mk_le_sum

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No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (weak)
5127	1	exposed public sections

Current commit 12137923ca
Reference commit 40d045ae49

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.py 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).

[felixpernegger]

LLM-generated

[NoneMore]

Thanks for the review!

[NoneMore]

-awaiting-author

[YaelDillies]

Thanks! 🚀

maintainer merge

[github-actions]

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