feat(PresentedGroup): free-product of presentations is isomorphic to the presentation of the union (over the disjoint union of generators)

[j-mayoral]

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Adds the theorem that the free product of presentations is isomorphic to the presentation on the disjoint union of the generators with the union of the relations. That is,
<α | R₁> * <β | R₂> ≃* <α ⊕ β | iα(R₁) ∪ iβ(R₂)>.

Don't know if the current file is the best to add this result.

I have the feeling this could be made more elegant, avoiding the need to state lemmas explicitly about the relations of the canonical maps, by instead working with relations on the free product of free groups and then studying how quotienting by relations behaves in terms of isomorphisms. However, that approach is less straightforward, so I prefer to keep the current PR as is and discuss possible refinements there to get better feedback (I’m new and still learning).

[github-actions]

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[github-actions]

PR summary 60ff4cd38c

Import changes exceeding 2%

%	File
+15.63%	Mathlib.GroupTheory.PresentedGroup

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.GroupTheory.PresentedGroup	467	540	+73 (+15.63%)

Import changes for all files

Files	Import difference
3 files Mathlib.GroupTheory.Coxeter.Basic Mathlib.GroupTheory.Coxeter.Inversion Mathlib.GroupTheory.Coxeter.Length	2
Mathlib.GroupTheory.PresentedGroup	73

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Declarations diff

+ coprodOf
+ coprodOf_kills_rels
+ coprodPresentations
+ lift_coprodOf_inl_eq_inl_mk
+ lift_coprodOf_inr_eq_inr_mk
+ lift_of_eq_mk_map
+ map_in_rels_eq_one

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 technical debt.

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).