feat: the product of two sums in a nonarchimedean ring

[trivial1711]

trafficstars

We prove that in a nonarchimedean ring, $$\sum_{(i, j) \in I \times J} a_i b_j = \left(\sum_{i \in I} a_i \right)\left(\sum_{j \in J} b_j\right),$$ provided that both sums on the right-hand side converge unconditionally.

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• [ ] depends on: #11998
• [ ] depends on: #12313
• [x] depends on: #12669

[github-actions[bot]]

PR summary e0dcb009db

Import changes exceeding 2%

%	File
+5.49%	Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean	1056	1114	+58 (+5.49%)

Import changes for all files

Files	Import difference
Mathlib.NumberTheory.Padics.MahlerBasis	5
Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean	58

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Declarations diff

+ HasSum.mul_of_nonarchimedean + Summable.mul_of_nonarchimedean + tsum_mul_tsum_of_nonarchimedean

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#11998~~
• ~~leanprover-community/mathlib4#12313~~
• ~~leanprover-community/mathlib4#12669~~ By Dependent Issues (🤖). Happy coding!

[trivial1711]

Thanks for the feedback.

[github-actions[bot]]

🚀 Pull request has been placed on the maintainer queue by eric-wieser.

[mathlib-bors[bot]]

Pull request successfully merged into master.

Build succeeded!

And happy new year! 🎉

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