feat: diffeomorphisms M ⊕ N ≃ N ⊕ M and friends

[grunweg]

Prove that the disjoint union of smooth manifolds is commutative, associative and has an empty manifold as neutral element --- all up to diffeomorphisms, i.e. M ⊕ N is diffeomorphic to N ⊕ M, etc.

From my bordism theory project: up to lots of API (which will be added in future PRs), this essentially shows that addition on the cobordism group is well-defined, associative and has the empty manifold as neutral element.

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Future: show distributivity with products. One smoothness direction is easy, the other is not obvious --- my current plan is to prove that it is bijective (since an equivalence) and a local diffeomorphism (since a top. embedding and an immersion between equi-dimensional manifolds), and deduce it from that. This will require some more results about local diffeomorphisms to land in mathlib.

[github-actions]

PR summary 5a7d7e1fc0

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

+ sumAssoc
+ sumAssoc_coe
+ sumComm
+ sumComm_coe
+ sumComm_inl
+ sumComm_inr
+ sumComm_symm
+ sumCongr
+ sumCongr_coe
+ sumCongr_inl
+ sumCongr_inr
+ sumCongr_symm_symm
+ sumEmpty
+ sumEmpty_toEquiv

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.

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No changes to technical debt.

You can run this locally as

./scripts/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).

[sgouezel]

LGTM, thanks!
bors d+

[mathlib-bors]

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

[grunweg]

Thanks for the review!
bors merge

[mathlib-bors]

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