feat: mvfderiv_const_smul and friends

[grunweg]

This generalises an existing mathlib lemma (as the differentiability hypothesis is in fact not necessary). At the same this, this specialises the lemma mvfderiv_smul to the case of the first factor being a constant.

Proper version of #34262.
This was developed as part of the path to the Levi-Civita connection, but wound up not being strictly necessary for its development.

Co-authored-by: Patrick Massot patrickmassot@free.fr

---

• depends on: chore: golf mvfderiv(Within)_zero #43986
• depends on: chore: reorder mvfderiv lemmas #43987

[github-actions]

PR summary ce93e090f6

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ mvfderivWithin_const_smul
+ mvfderivWithin_zero_of_not_mdifferentiableWithinAt
+ mvfderiv_const_smul
+ mvfderiv_zero_of_not_mdifferentiableAt
+ smul_def

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 -- stale, waiting for the new build)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 6daaf79).

• +6 new declarations
• −0 removed declarations

+mvfderivWithin_const_fun_smul
+mvfderivWithin_const_smul
+mvfderivWithin_zero_of_not_mdifferentiableWithinAt
+mvfderiv_const_fun_smul
+mvfderiv_const_smul
+mvfderiv_zero_of_not_mdifferentiableAt

---

No changes to strong technical debt.
No changes to weak technical debt.

Current commit ce93e090f6
Reference commit 158047ba1d

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.py 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:

• chore: golf mvfderiv(Within)_zero #43986
• chore: reorder mvfderiv lemmas #43987
  By Dependent Issues (🤖). Happy coding!