[Merged by Bors] - feat: add contDiffWithinAt_clm_apply

[mathlib-splicebot]

All the necessary work as already contained in contDiffOn_clm_apply; it is useful to also have the point-wise version available. This will be used to prove a smoothness criterion of tensor fields on manifold.

From the path towards the smoothness of the Levi-Civita connection.

[github-actions]

PR summary 52f1a4c105

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ contDiffWithinAt_clm_apply

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 52f1a4c).

• +1 new declarations
• −0 removed declarations

+contDiffWithinAt_clm_apply

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 52f1a4c105
Reference commit 5edf93c0f3

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).

[j-loreaux]

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Post-Build Step
• ci (staging) / Test and lint
• ci (staging) / Post-CI job
• ci (staging) / Lint style
• ci (staging) / Build