[Merged by Bors] - feat: final lemmas needed for showing gaussNorm on MvPowerSeries is an absolute value

[WilliamCoram]

We finish our section on showing that the gaussNorm on MvRestricted power series will be an absolute value by giving the neg and mul_eq_mul lemmas.

---

[github-actions]

PR summary fe138269c9

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ gaussNorm_mul_eq_mul
+ gaussNorm_neg

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 fe13826).

• +2 new declarations
• −0 removed declarations

+MvPowerSeries.gaussNorm_mul_eq_mul
+MvPowerSeries.gaussNorm_neg

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit fe138269c9
Reference commit b9251c8115

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!

[riccardobrasca]

Thanks!

bors d+

[mathlib-bors]

✌️ WilliamCoram can now approve this pull request until 2026-07-09 09:21 UTC (in 2 weeks). To approve and merge, reply with bors r+. More detailed instructions are available here.

⚠️ This delegation only covers changes within Archive/**, Counterexamples/**, docs/**, DownstreamTest/**, Mathlib/**, MathlibTest/**, widget/**, Archive.lean, Counterexamples.lean, docs.lean, Mathlib.lean; an author commit touching anything else will revoke it. Bors also revokes it if a later push changes too many files for it to check the full list — even if it stays within scope.

[WilliamCoram]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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