feat: a diffeomorphism induces a manifold structure

[Bergschaf]

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This PR adds the pullback of a ChartedSpace instance along a Homeomorphism. (Similar to IsLocalHomeomorph.chartedSpace but with better def-eqs (because there is no need to choose the inverse of the function in this case)).
Diffeomorph.isManifold proves that the pullback of the ChartedSpace of a manifold along a diffeomorphism is a manifold again.
I am quite new to this area of mathlib, so please excuse any obvious oversights on my part.
Please give me feedback if this definition is appropriate!

[mathlib-bors]

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[mathlib-bors]

This pull request is now in draft mode. No active bors state needed cleanup.

While this PR remains draft, bors will ignore commands on this PR. Mark it ready for review before using commands like bors r+ or bors try.

[github-actions]

PR summary 1e9e1fee3c

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

+ Homeomorph.chartedSpace
+ isManifold

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 1e9e1fee3c
Reference commit 1450d19e6f

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).

[grunweg]

Thanks for your contribution; differential geometry definitely needs more helping hands!
This PR adds a new definition, but no API (lemmas about it, or even results convincing that this is the right definition). Can you say why you want to have this definition? Do you have any application in mind?

[grunweg]

This is a bit of a strange condition and statement. (I would assume that makes it awkward to use in practice.) Why do you write it like this?
Is it that you want to write "let f be a diffeomorphism from M' to M", but that statement requires a charted space structure on M' to make sense?

[grunweg]

A more natural statement would be the following:
Let f be a homeomorphism from M' to M. Endow M' with the charted space structure (via pullback). Then M' is a manifold w.r.t. the same model with corners as M, and this smooth structure makes f a smooth map (and even a diffeomorphism).

[grunweg]

Note that #39107 has the same construction, but re-using the version for local homeomorphisms.