feat(RingTheory): etale lifting property of henselian local rings

[erdOne]

---

[github-actions]

PR summary a3b4e38671

Import changes exceeding 2%

%	File
+79.49%	Mathlib.RingTheory.Henselian

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.RingTheory.Henselian	1385	2486	+1101 (+79.49%)
Mathlib.RingTheory.Idempotents	1201	1202	+1 (+0.08%)

Import changes for all files

Files	Import difference
Mathlib.RingTheory.Idempotents	1
Mathlib.RingTheory.Henselian	1101

---

Declarations diff (regex)

+ HenselianLocalRing.algEquivEquiv
+ HenselianLocalRing.eq_of_residueFieldMap_eq
+ HenselianLocalRing.exist_algEquiv_residueFieldMap_eq_of_etale
+ HenselianLocalRing.exist_residueFieldMap_eq_of_etale
+ HenselianLocalRing.exists_completeOrthogonalIdempotents_forall_isLocalRing
+ HenselianLocalRing.ofId_comp_bijective
+ HenselianLocalRing.of_finite
+ HenselianLocalRing.of_finite_aux
+ IsIdempotentElem.ker_toCorner
+ IsIdempotentElem.toCorner_surjective
+ finrank_eq_one_iff_algebraMap_bijective
+ instance : IsLocalHom e.toAlgHom := ⟨by simp⟩
+ instance : IsLocalHom e.toAlgHom.toRingHom := ⟨by simp⟩
+ instance : IsLocalHom e.toRingEquiv.toRingHom := ⟨by simp⟩
+ instance {R R' S : Type*} [CommSemiring R] [CommSemiring R'] [Semiring S] [Algebra R S]
+ instance {R S : Type*} [CommRing R] [CommRing S] [Algebra R S] [IsLocalRing R]
+ instance {R S : Type*} [CommSemiring R] [Semiring S] [Algebra R S]
- instance : IsLocalHom e.toAlgHom := by

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 a3b4e38).

• +15 new declarations
• −0 removed declarations

+AlgEquiv.instIsLocalHomRingHomToAlgHom
+AlgEquiv.instIsLocalHomRingHomToRingHomToRingEquiv
+HenselianLocalRing.algEquivEquiv
+HenselianLocalRing.eq_of_residueFieldMap_eq
+HenselianLocalRing.exist_algEquiv_residueFieldMap_eq_of_etale
+HenselianLocalRing.exist_residueFieldMap_eq_of_etale
+HenselianLocalRing.exists_completeOrthogonalIdempotents_forall_isLocalRing
+HenselianLocalRing.ofId_comp_bijective
+HenselianLocalRing.of_finite
+IsIdempotentElem.ker_toCorner
+IsIdempotentElem.toCorner_surjective
+Module.finrank_eq_one_iff_algebraMap_bijective
+instAlgebraCorner
+instIsLocalHomRingHomAlgebraMapOfIsLocalRingOfIsIntegralOfNontrivial
+instIsScalarTowerCorner

---

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

Current number	Change	Type (strong)
5690	1	backward.isDefEq.respectTransparency

No changes to weak technical debt.

Current commit a3b4e38671
Reference commit 571b8a8e54

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).