feat: presented monoids

[hannahfechtner]

Define presented monoids and their universal property. This requires some additions to free monoids, and GroupTheory/Congruence

---

• [ ] depends on: #17180

[github-actions[bot]]

PR summary 4217a11a85

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Algebra.PresentedMonoid.Basic	428

---

Declarations diff

+ PresentedMonoid + closure_range_of + ext + inductionOn + inductionOn₂ + inductionOn₃ + instance {rels : FreeMonoid α → FreeMonoid α → Prop} : Monoid (PresentedMonoid rels) + lift + lift_of + mk + of + surjective_mk + toMonoid.unique

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

[erdOne]

Also please merge master in case of merge conflicts. Thanks!

[YaelDillies]

I think people who are not interested in presented monoids might be interested in the parts I'm asking you to split off.

[erdOne]

Hey sorry for abandoning this for so long. I agree with Yael that the more useful part are the monoid API and I might not be the best person to review those. But I could review the rest of this PR once that lands.

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#17180~~ By Dependent Issues (🤖). Happy coding!

[erdOne]

LGTM Thanks! maintainer merge

[github-actions[bot]]

🚀 Pull request has been placed on the maintainer queue by erdOne.

[mathlib-bors[bot]]

This PR was included in a batch that was canceled, it will be automatically retried

[mathlib-bors[bot]]

Already running a review

[Vierkantor]

Oops, I could swear I reloaded this page before borsing. Anyway, I'll give this a

bors d+

in case the build ends up failing.

[mathlib-bors[bot]]

:v: hannahfechtner can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[mathlib-bors[bot]]

Pull request successfully merged into master.

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