[Merged by Bors] - feat(RingTheory/Ideal): prove transitivity for the relative norm

[xroblot]

Let R ⊆ S ⊆ T be a tower of rings and I : Ideal T, then relNorm R I = relNorm R (relNorm S I)

Also, add the relNorm version of spanNorm_le_comap that was forgotten in a previous PR.

---

• depends on: [Merged by Bors] - feat: add Mathlib.RingTheory.DedekindDomain.Instances #26070
• depends on: [Merged by Bors] - feat(DedekindDomain): More instances #28526

[github-actions]

PR summary 0a6e2f47d0

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.RingTheory.IntegralClosure.IntegralRestrict	1916	1917	+1 (+0.05%)
Mathlib.RingTheory.Ideal.Norm.RelNorm	2000	2001	+1 (+0.05%)

Import changes for all files

Files

Import difference

10 files Mathlib.NumberTheory.NumberField.Discriminant.Different Mathlib.NumberTheory.RamificationInertia.Galois Mathlib.RingTheory.DedekindDomain.Different Mathlib.RingTheory.Frobenius Mathlib.RingTheory.Ideal.Norm.RelNorm Mathlib.RingTheory.IntegralClosure.IntegralRestrict Mathlib.RingTheory.Invariant.Basic Mathlib.RingTheory.Invariant.Profinite Mathlib.RingTheory.Invariant Mathlib.RingTheory.Trace.Quotient

1

---

Declarations diff

+ Algebra.intNorm_intNorm
+ instance (B C : Type*) [CommRing B] [IsDomain B] [CommRing C] [IsDomain C] [Algebra A B]
+ le_spanNorm_spanNorm
+ relNorm_le_comap
+ relNorm_relNorm
+ spanNorm_spanNorm
+ spanNorm_spanNorm_of_bot_or_top

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-bot-assistant]

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

[mathlib4-merge-conflict-bot]

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

[mathlib4-merge-conflict-bot]

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

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat: add Mathlib.RingTheory.DedekindDomain.Instances #26070
• [Merged by Bors] - feat(DedekindDomain): More instances #28526
  By Dependent Issues (🤖). Happy coding!

[riccardobrasca]

Thanks!

bors d+

[mathlib-bors]

✌️ xroblot can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[kbuzzard]

The lint error is an issue with simp says and it seems that an acceptable fix is to just replace the call with a simp only call and delete the says stuff.

[xroblot]

The lint error is an issue with simp says and it seems that an acceptable fix is to just replace the call with a simp only call and delete the says stuff.

There are in fact several calls to simp says that produce some errors. I am trying to collect them and fix them here: #28775

[xroblot]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• CI Success