feat: immersed points

[grunweg]

Define immersed points of a (differentiable) map between manifolds, and prove that immersed points compose.

Future PRs show that x is an immersed point of f if and only if f is an immersion at x:
thus, proving the composition of immersed points (which follows immediately from the chain rule)
implies the composition of immersions (which is not obvious from their definition.

From the path towards immersions, embeddings and submanifolds.

---

• depends on: [Merged by Bors] - feat: equivalent characterisation of split continuous linear maps #35057
• depends on: [Merged by Bors] - feat: add (m)differentiableAt_of_(m)fderiv_injective #35284

[github-actions]

PR summary af1b8b4417

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Geometry.Manifold.ImmersedPoint (new file)	2245

---

Declarations diff

+ Diffeomorph.isInvertible_mfderiv
+ IsImmersedPoint
+ IsLocalDiffeomorph.isInvertible_mfderiv
+ IsLocalDiffeomorphAt.isInvertible_mfderiv
+ _root_.IsLocalDiffeomorphAt.isImmersedPoint
+ comp
+ comp_isLocalDiffeomorphAt_left
+ comp_isLocalDiffeomorphAt_left_iff
+ comp_isLocalDiffeomorphAt_right
+ comp_isLocalDiffeomorphAt_right_iff
+ congr
+ continuousAt
+ continuousAt_localInverse
+ isImmersedPoint_iff
+ mdifferentiableAt
+ mfderiv_injective
+ of_comp
+ of_injective_of_finiteDimensional
+ of_mfderiv_isInvertible

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 scripts/declarations_diff.sh contains some details about this script.

---

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).

[mathlib-merge-conflicts]

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

[mathlib-merge-conflicts]

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

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat: equivalent characterisation of split continuous linear maps #35057
• [Merged by Bors] - feat: add (m)differentiableAt_of_(m)fderiv_injective #35284
  By Dependent Issues (🤖). Happy coding!