feat(Algebra/Order/Antidiagonal): connect Finset.HasAntidiagonal with Filter.TendstoCofinite

[BryceT233]

This PR connects Finset.HasAntidiagonal with Filter.TendstoCofinite and cleans up TendstoCofinite.lean.

---

• depends on: chore(Algebra/Order/Antidiag): relax an assumption in the definition of HasAntidiagonal #41521

[github-actions]

PR summary 93342b0ed9

Import changes exceeding 2%

%	File
+49.60%	Mathlib.Algebra.Order.Antidiag.Tendsto

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.Order.Antidiag.Tendsto	623	932	+309 (+49.60%)

Import changes for all files

Files	Import difference
Mathlib.RingTheory.MvPowerSeries.Restricted	1
Mathlib.Algebra.Order.Antidiag.Tendsto	309

---

Declarations diff (regex)

+ coe_mulAntidiagonal_eq_preimage_singleton
+ hasMulAntidiagonal
+ instance [Mul A] : Subsingleton (HasMulAntidiagonal A)
+ tendstoCofinite_mul
- instance [Monoid A] : Subsingleton (HasMulAntidiagonal A)

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 -- unavailable)

⚠️ The Mathlib cache for this PR's merge-base isn't on the server (typically a bors-batch intermediate that CI never built). Merge master into this PR and push to refresh.

---

No changes to strong technical debt.

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

Current number	Change	Type (weak)
5005	-1	exposed public sections

Current commit 93342b0ed9
Reference commit e3b73828b0

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-dependent-issues]

This PR/issue depends on:

• chore(Algebra/Order/Antidiag): relax an assumption in the definition of HasAntidiagonal #41521
  By Dependent Issues (🤖). Happy coding!

[BryceT233]

I noticed the tech debt label was triggered. This is likely because I removed an @[expose] attribute in a leaf file that doesn't contain any definitions. Is this removal actually recommended, or would it be better to revert this?

[plp127]

I noticed the tech debt label was triggered. This is likely because I removed an @[expose] attribute in a leaf file that doesn't contain any definitions. Is this removal actually recommended, or would it be better to revert this?

The tech debt decreased, so this is good. Indeed since there are no definitions in that file, @[expose] isn't doing anything.