feat(Topology/Algebra): inv and div for infinite products over groups with zero

[ajirving]

Proves two lemmas for infinite products over groups with zero: inverses and division behave as expected provided the limit is nonzero. This requires an extra import to get some of the GroupWithZero API. Maybe the GroupWithZero results should be in a different file but I was just adding to what was already there in Group.lean.

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[github-actions]

PR summary cf8b53ebcc

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Algebra.InfiniteSum.Group	1136	1137	+1 (+0.09%)

Import changes for all files

Files	Import difference
6 files Mathlib.Topology.Algebra.InfiniteSum.Constructions Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution Mathlib.Topology.Algebra.InfiniteSum.GroupCompletion Mathlib.Topology.Algebra.InfiniteSum.Group Mathlib.Topology.Algebra.InfiniteSum.Module Mathlib.Topology.Algebra.InfiniteSum.NatInt	1

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Declarations diff (regex)

+ HasProd.div₀
+ HasProd.inv₀

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 cf8b53e).

• +2 new declarations
• −0 removed declarations

+HasProd.div₀
+HasProd.inv₀

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit cf8b53ebcc
Reference commit 0c9776382e

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!

[plp127]

Can you generalize these lemmas to an arbitrary SummationFilter, instead of just .unconditional?

[ajirving]

Can you generalize these lemmas to an arbitrary SummationFilter, instead of just .unconditional?

Thanks, I've done that now.