feat(RingTheory/LaurentSeries): add Leibniz rule

[mo271]

This adds hasseDeriv_mul and derivative_mul.

Written with the help of Gemini

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[github-actions]

PR summary 0ecab2aa3c

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)

+ derivative_mul
+ hasseDeriv_mul

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 0ecab2a).

• +2 new declarations
• −0 removed declarations

+LaurentSeries.derivative_mul
+LaurentSeries.hasseDeriv_mul

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 0ecab2aa3c
Reference commit 2eecc3c0ec

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).

[github-actions]

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!

[mathlib-bors]

This pull request is now in draft mode. No active bors state needed cleanup.

While this PR remains draft, bors will ignore commands on this PR. Mark it ready for review before using commands like bors r+ or bors try.

[felixpernegger]

--h ?

[mo271]

This is a comment about the named placeholders to not get disoriented when going through the 4 cases

refine Finset.sum_bij (fun x _ => (x.1 - (ij.1 : ℤ), x.2 - (ij.2 : ℤ))) ?hi ?inj ?surj ?h

Should I remove those?

[wwylele]

Is it possible to link hasseDeriv to iterated Derivation, then prove the multiplication formula there? (I haven't check thoroughly how much of this is already done)