feat(RingTheory.DedekindDomain.Factorization): add API for factorization

[MichaelStollBayreuth]

This PR adds

• simp lemmas that convert ways of expressing the multiplicity of a prime ideal p in the factorization of an ideal I into multiplicity p.asIdeal I (see #Is there code for X? > Results on elements of number fields and ideals @ 💬),
• API lemmas on multiplicities, expressed in terms of multiplicity p.asIdeal I.
• We also refactor a proof in Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas by extracting a couple of lemmas that we can reuse in one of the new lemmas.

These will be useful in proving the Northcott property of heights on number fields.

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[github-actions]

PR summary 900c9b0390

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.RingTheory.DedekindDomain.Factorization	2126	2127	+1 (+0.05%)

Import changes for all files

Files

Import difference

19 files Mathlib.Algebra.Module.Torsion.PrimaryComponent Mathlib.AlgebraicGeometry.EllipticCurve.LFunction Mathlib.NumberTheory.FLT.Three Mathlib.NumberTheory.Height.NumberField Mathlib.NumberTheory.NumberField.AdeleRing Mathlib.NumberTheory.NumberField.Completion.FinitePlace Mathlib.NumberTheory.NumberField.Cyclotomic.Basic Mathlib.NumberTheory.NumberField.Cyclotomic.Galois Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal Mathlib.NumberTheory.NumberField.Cyclotomic.PID Mathlib.NumberTheory.NumberField.Cyclotomic.Three Mathlib.NumberTheory.NumberField.Discriminant.Different Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.NumberTheory.NumberField.Ideal.Basic Mathlib.NumberTheory.NumberField.ProductFormula Mathlib.RingTheory.DedekindDomain.Factorization Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing Mathlib.RingTheory.Ideal.Norm.RelNorm Mathlib.Topology.Algebra.Ring.Compact

1

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Declarations diff

+ Ideal.finprod_heightOneSpectrum_pow_multiplicity
+ count_normalizedFactors_eq_multiplicity
+ emultiplicity_ciSup
+ emultiplicity_sup
+ factorization_eq_multiplicity
+ maxPowDividing_eq_pow_multiplicity
+ multiplicity_ciSup
+ multiplicity_le_of_ideal_ge
+ multiplicity_sup
+ normalizedFactors_prod_inter_eq_inter
+ prod_inter_normalizedFactors_ne_zero

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.

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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).