chore(FractionRing): generalize an instance

[xroblot]

The instance that deduce from a tower of domains A ⊆ B ⊆ C that there is a tower Frac A ⊆ Frac B ⊆ Frac C can be generalized to A ⊆ B ⊆ K implies Frac A ⊆ Frac B ⊆ K where K is a field (and exactly the same proof works!).

---

[github-actions]

PR summary 14d639db18

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ instance (B K : Type*) [CommRing B] [IsDomain B] [Field K] [Algebra A B]
- instance (B C : Type*) [CommRing B] [IsDomain B] [CommRing C] [IsDomain C] [Algebra A B]

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/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).

[leanprover-community-mathlib4-bot]

!bench

[leanprover-bot]

Here are the benchmark results for commit 632367e.
There were no significant changes against commit 14d639d.

[github-actions]

File	Instructions	%
build	+9.190⬝10⁹	(+0.00%)
Mathlib.RingTheory.IntegralClosure.IntegralRestrict	+3.259⬝10⁹	(+1.21%)
Mathlib.AlgebraicGeometry.GammaSpecAdjunction	+1.52⬝10⁹	(+1.38%)
Mathlib.RingTheory.Localization.FractionRing	-5.419⬝10⁹	(-8.94%)
CI run Lakeprof report

[grunweg]

Sure, why not? Benchmarking seems fine. But a close look by an algebraist would be good.
maintainer merge?

[github-actions]

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

[jcommelin]

This isn't a strict generalization, right?

On the one hand, the goal is now more flexible, it can be any field K, but on the other hand, K now also appears as field amongst the assumptions, whereas C only had to be a domain.

[xroblot]

This isn't a strict generalization, right?

On the one hand, the goal is now more flexible, it can be any field K, but on the other hand, K now also appears as field amongst the assumptions, whereas C only had to be a domain.

Well, what I meant is that Lean can deduce the original instance from the new one since IsScalarTower A B C implies IsScalarTower A B (FractionRing C) thanks to OreLocalization.instIsScalarTower