feat(RingTheory/RamificationInertia/Basic): ramification-inertia formula for finite flat extensions

[tb65536]

This PR proves the ramification-inertia formula for finite flat extensions.

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• depends on: feat(RingTheory/Spectrum/FreeLocus): rank of fiber over residue field #38825
• depends on: feat(FieldTheory/Galois/IsGaloisGroup): generalize finiteness of Galois groups from fields to rings #39094
• depends on: feat(RingTheory/LocalRing/ResidueField/Fiber): the localization of Ideal.Fiber is a quotient #39196

[github-actions]

PR summary 38c35d74ba

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RingTheory.RamificationInertia.Basic (new file)	2368

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Declarations diff

+ Fiber.localizationAlgEquivQuotient
+ IsGaloisGroup.to_isFractionRing_of_isIntegral
+ _root_.Ideal.finrank_fiber_eq_finrank
+ foo3
+ isInvariant_of_isIntegral
+ sum_ramification_inerta_eq_finrank
+ sum_ramification_inertia_eq_card
+ sum_ramification_inertia_eq_finrank_fiber

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 strong technical debt.

No changes to weak technical debt.

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(RingTheory/Spectrum/FreeLocus): rank of fiber over residue field #38825
• feat(FieldTheory/Galois/IsGaloisGroup): generalize finiteness of Galois groups from fields to rings #39094
• feat(RingTheory/LocalRing/ResidueField/Fiber): the localization of Ideal.Fiber is a quotient #39196
  By Dependent Issues (🤖). Happy coding!