feat: isInvertible_mfderiv_extend

[grunweg]

Prove that extended charts have invertible mfderiv, provided they lie in a maximal atlas.
This generalises isInvertible_mfderiv_extChartAt and its preliminary lemmas to any extended chart in the maximal atlas: this will be used in #41796 to prove that immersions have immersed points.

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• depends on: [Merged by Bors] - chore: golf proofs of mdifferentiableAt_atlas{_symm} #42011

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[github-actions]

PR summary cf889da53c

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)

+ OpenPartialHomeomorph.mdifferentiableAt_extend
+ OpenPartialHomeomorph.mdifferentiableOn_extend
+ isInvertible_mfderivWithin_extend_symm
+ isInvertible_mfderiv_extend
+ mdifferentiableOn_extend_symm
+ mdifferentiableWithinAt_extend_symm
+ mfderivWithin_extend_symm_comp_mfderiv_extend
+ mfderivWithin_extend_symm_comp_mfderiv_extend'
+ mfderiv_extend_comp_mfderivWithin_extend_symm
+ mfderiv_extend_comp_mfderivWithin_extend_symm'

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)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit cf889da).

• +10 new declarations
• −0 removed declarations

+OpenPartialHomeomorph.mdifferentiableAt_extend
+OpenPartialHomeomorph.mdifferentiableOn_extend
+isInvertible_mfderivWithin_extend_symm
+isInvertible_mfderiv_extend
+mdifferentiableOn_extend_symm
+mdifferentiableWithinAt_extend_symm
+mfderivWithin_extend_symm_comp_mfderiv_extend
+mfderivWithin_extend_symm_comp_mfderiv_extend'
+mfderiv_extend_comp_mfderivWithin_extend_symm
+mfderiv_extend_comp_mfderivWithin_extend_symm'

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit cf889da53c
Reference commit 7779d601f7

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).

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - chore: golf proofs of mdifferentiableAt_atlas{_symm} #42011
  By Dependent Issues (🤖). Happy coding!