chore: golf FormalMultilinearSeries.fderiv_sum

[kim-em]

This PR golfs the proof of FormalMultilinearSeries.fderiv_sum to use the existing API lemma HasFPowerSeriesOnBall.sum, instead of re-deriving it via hasSum/tsum_eq and unfolding the definition of FormalMultilinearSeries.sum with rw.

Follow-up to #41018 (feat(Analysis): lemma for fderiv of FormalMultilinearSeries.sum).

🤖 Prepared with Claude Code

[github-actions]

PR summary a6d5aafdaa

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)

No declarations were harmed in the making of this PR! 🐙

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 a6d5aaf).

• +0 new declarations
• −0 removed declarations

No declaration differences.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit a6d5aafdaa
Reference commit a33a5ccd63

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).