feat(RingTheory/LocalRing): IsLocalRing for pullbacks

[BryceT233]

We provide basic lemmas for equalizers and pullbacks of RingHom and AlgHom, and show they are local rings under suitable condtions.

This is needed in #37940 to construct a residue algebra structure on pullbacks.

---

[github-actions]

PR summary 977f84bd6e

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RingTheory.LocalRing.Pullback (new file)	1202

---

Declarations diff

+ isLocalHom_pullbackFst
+ isLocalHom_pullbackSnd
+ isLocalRing_eqLocus
+ isUnit_eqLocus_mk_iff
++ isLocalRing_pullback
++ isUnit_pullback_mk_iff
++ pullback
++ pullbackFst
++ pullbackSnd
++ pullback_comm_sq
++ surjective_pullbackFst_of_surjective
++ surjective_pullbackSnd_of_surjective

You can run this locally as follows

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

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

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

---

No changes to technical debt.

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).

[BryceT233]

I heard about IsLocalHom is a bad instance and I am not very sure how to use it, I used it as a instance above but not here, probably this is not ideal.