feat(CategoryTheory/Presentable): lemmas about sharply smaller regular cardinals

[joelriou]

---

[github-actions]

PR summary eba1c9f7c0

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Presentable.SharplyLT.Lemmas (new file)	1040

---

Declarations diff (regex)

+ exists_le_of_small
+ exists_of_pair
+ exists_of_small
+ exists_of_triple
+ fromSigma
+ fromSigma_surjective
+ mk_iio_le_lift
+ of_le
+ of_pow_lt

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 eba1c9f).

• +9 new declarations
• −0 removed declarations

+Cardinal.SharplyLT.exists_of_pair
+Cardinal.SharplyLT.exists_of_small
+Cardinal.SharplyLT.exists_of_triple
+Cardinal.SharplyLT.of_le
+Cardinal.SharplyLT.of_pow_lt
+Cardinal.exists_le_of_small
+Cardinal.mk_iio_le_lift
+CategoryTheory.CardinalDirectedPoset.SetCardinalLT.fromSigma
+CategoryTheory.CardinalDirectedPoset.SetCardinalLT.fromSigma_surjective

---

No changes to strong technical debt.

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

Current number	Change	Type (weak)
4932	1	exposed public sections

Current commit eba1c9f7c0
Reference commit dda78df98c

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).