feat: immersions are locally embeddings

[grunweg]

Hopefully, this can be used for the topological portion of #28865. (That part is not certain yet, the rest works.)

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Needs some clean-up in both the immersions file, and need to move the helper results about embeddings to the correct location.

• depends on: [Merged by Bors] - feat: smooth immersions #28793
• depends on: [Merged by Bors] - feat: immersions are smooth #28796
• depends on: [Merged by Bors] - feat: product of immersions is an immersion #28853

[github-actions]

PR summary 767088cede

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 (regex)

+ IsEmbedding.subtype_map_of_subset
+ _root_.Topology.IsEmbedding.comp_restrict
+ isClosedEmbedding_symm_restrict
+ isEmbedding_extend_restrict
+ isEmbedding_extend_symm_restrict
+ isEmbedding_restr_domChart_source
+ isEmbedding_symm_restrict
+ rightInverse_restrict
++ eqOn_domChart_source
++ exists_nbhd_restr_isEmbedding

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.

Declarations diff (Lean -- pending)

Computed after the build finishes.

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 767088cede
Reference commit 433572dde7

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).

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat: smooth immersions #28793
• [Merged by Bors] - feat: immersions are smooth #28796
• [Merged by Bors] - feat: product of immersions is an immersion #28853
  By Dependent Issues (🤖). Happy coding!

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.