feat(Analysis/Normed): norm and Multiset.prod commute

[wwylele]

Similar to Finset.prod lemmas above, provides convenient rewriting lemma.

---

[wwylele]

easy

[github-actions]

PR summary 911b636566

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ Multiset.nnnorm_prod_map
+ Multiset.norm_prod_map

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 911b636).

• +4 new declarations
• −0 removed declarations

+Multiset.nnnorm_prod_map
+Multiset.norm_prod_map
+nnnormHom.congr_simp
+normHom.congr_simp

---

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

Current commit 911b636566
Reference commit fd634dd297

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).