feat(Tactic/Group): strengthen the group tactic and add tests

[AlexBrodbelt]

The group tactic is improved to:

Once simplification on the exponents is done, apply left and right cancellation. That is, to normalise expressions like a * b = a * c to b * c.

Apply a post-processing where expression of the form ( · )^(-1) are normalised to use the inversion notation ( · )⁻¹. This allows immediately using lemmas involving inversion which is how most lemmas are stated.

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[github-actions]

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[github-actions]

PR summary a2f58acf35

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

No declarations were harmed in the making of this PR! 🐙

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.

Current commit a2f58acf35
Reference commit 0531bb79fe

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).

[github-actions]

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!

[grunweg]

Once your PR is complete, I'm very curious to see if there is any performance effect. But that can wait for later. Until then, I'm just excited about your PR!