feat(NumberTheory/NumberField/Ideal/KummerDedekind): start from a prime rather than from a factor

[xroblot]

The two Kummer-Dedekind lemmas giving the ramification index and the residual degree are stated for the ideal attached to a factor of the minimal polynomial. Starting instead from a prime above p, as one usually does, means going through the equivalence and back. This adds the two statements in that direction, and uses them to shorten the two proofs in Cyclotomic/Ideal.lean that were doing the round trip by hand.

It also adds a few lemmas unfolding what it means to belong to monicFactorsMod.

Prepared with Claude Code 🤖

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[github-actions]

PR summary ef4be1f127

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff (regex)

+ inertiaDeg_primesOverSpanEquivMonicFactorsMod_apply
+ irreducible_monicFactorsMod
+ mem_monicFactorsMod_iff
+ monicFactorsMod_dvd_map_minpoly
+ monic_monicFactorsMod
+ ramificationIdx_primesOverSpanEquivMonicFactorsMod_apply

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 ef4be1f).

• +6 new declarations
• −0 removed declarations

+NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_apply
+NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_apply
+RingOfIntegers.irreducible_monicFactorsMod
+RingOfIntegers.mem_monicFactorsMod_iff
+RingOfIntegers.monicFactorsMod_dvd_map_minpoly
+RingOfIntegers.monic_monicFactorsMod

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No changes to strong technical debt.
No changes to weak technical debt.

Current commit ef4be1f127
Reference commit c58b47adb3

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.py 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).