feat(GroupTheory/Commutator/Basic): ⁅H₁, H₂⁆ is a normal subgroup of H₁ ⊔ H₂

[SnirBroshi]

Shows ⁅H₁, H₂⁆ ≤ H₁ ⊔ H₂ and (⁅H₁, H₂⁆.subgroupOf <| H₁ ⊔ H₂).Normal, and adds _ ≤ normalizer _ ↔ lemmas to help.

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(from the book "Finite Groups" by Daniel Gorenstein)

Also renames AddSubgroup.mem_normalizer_iff_conj_image_eq because to_additive now renames conj to addConj and this theorem should stay in sync with its counterpart, even though it's not using to_additive because MulAut isn't additivized.

The proofs seem pretty long for such trivial lemmas, suggestions welcome :)

[github-actions]

PR summary 686c76b39d

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

+ _root_.AddSubgroup.le_normalizer_closure_iff
+ _root_.AddSubgroup.mem_normalizer_iff_addConj_image_eq
+ commutatorElement_mul_left_eq_conj_mul
+ commutatorElement_mul_right_eq_mul_conj
+ commutator_le_sup
+ le_normalizer_closure_iff
+ le_normalizer_iff
+ le_set_normalizer_iff
+ normal_subgroupOf_commutator_sup
- _root_.AddSubgroup.mem_normalizer_iff_conj_image_eq

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.