refactor: make adicCompletionIntegers a type

[smmercuri]

---

[github-actions]

PR summary 6de40ddd65

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ adicCompletionIntegers.valuationSubring
+ coe_add
+ coe_mk
+ coe_mul
+ coe_one
+ coe_zero
+ ext
+ instance : Algebra (adicCompletionIntegers K v) (v.adicCompletion K)
+ instance : Algebra R (adicCompletionIntegers.valuationSubring K v)
+ instance : CoeHead (adicCompletionIntegers K v) (v.adicCompletion K) := ⟨val K v⟩
+ instance : CommRing (FiniteAdeleRing R K) := inferInstanceAs <| CommRing <|
+ instance : IsFractionRing (adicCompletionIntegers K v) (v.adicCompletion K)
+ instance : IsLocalRing (v.adicCompletionIntegers K)
+ instance : TopologicalSpace (FiniteAdeleRing R K) := inferInstanceAs <| TopologicalSpace <|
+ instance : TopologicalSpace (adicCompletionIntegers K v)
+ instance : UniformSpace (adicCompletionIntegers K v)
+ val
- instance : CommRing (FiniteAdeleRing R K) := inferInstanceAs <|
- instance : TopologicalSpace (FiniteAdeleRing R K) := inferInstanceAs <|

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 6de40dd).

• +27 new declarations
• −9 removed declarations

+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.coe_add
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.coe_mk
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.coe_mul
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.coe_one
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.coe_zero
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.ext
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.ext_iff
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.instAlgebraAdicCompletion
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.instCoeHeadAdicCompletion
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.instInhabited
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.instIsFractionRingAdicCompletion
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.instTopologicalSpace
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.instUniformSpace
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.val
+IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.valuationSubring
+IsDedekindDomain.HeightOneSpectrum.instAlgebraAdicCompletionIntegers
-IsDedekindDomain.HeightOneSpectrum.instAlgebraSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers
+IsDedekindDomain.HeightOneSpectrum.instAlgebraSubtypeAdicCompletionMemValuationSubringValuationSubring
+IsDedekindDomain.HeightOneSpectrum.instCommRingAdicCompletionIntegers
+IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulAdicCompletionIntegers
+IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulAdicCompletionIntegersAdicCompletion
-IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers
-IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers_1
-IsDedekindDomain.HeightOneSpectrum.instInhabitedSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers
+IsDedekindDomain.HeightOneSpectrum.instIsDomainAdicCompletionIntegers
+IsDedekindDomain.HeightOneSpectrum.instIsTorsionFreeAdicCompletionIntegers
-IsDedekindDomain.HeightOneSpectrum.instIsTorsionFreeSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers
+IsDedekindDomain.HeightOneSpectrum.instNontrivialAdicCompletionIntegers
+LaurentSeries.instAlgebraAdicCompletionIntegersPolynomialRatFuncIdealX
-LaurentSeries.instAlgebraSubtypeAdicCompletionPolynomialRatFuncIdealXMemValuationSubringAdicCompletionIntegers
-RingEquiv.restrict.congr_simp
+instIsDiscreteValuationRingAdicCompletionIntegers
-instIsDiscreteValuationRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers
+instIsLocalRingAdicCompletionIntegers
+instIsPrincipalIdealRingAdicCompletionIntegers
-instIsPrincipalIdealRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 6de40ddd65
Reference commit 6f60478685

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).

[smmercuri]

!radar

[github-actions]

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!

[leanprover-radar]

Benchmark results for 6de40dd against 6f60478 are in. No significant results found. @smmercuri

• ✅ build//instructions: -298.7G (-0.19%)

Medium changes (2✅)

• ✅ build//instructions: -298.7G (-0.19%)
• ✅ build/module/Mathlib.NumberTheory.Padics.HeightOneSpectrum//instructions: -6.6G (-13.59%)

and 1 hidden

Small changes (2✅)

• ✅ build/module/Mathlib.RingTheory.DedekindDomain.AdicValuation//instructions: -2.2G (-2.31%)
• ✅ build/module/Mathlib.RingTheory.LaurentSeries//instructions: -6.3G (-4.02%)

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.