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.

---

[github-actions]

PR summary 3c6d1ffe9e

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Algebra.InfiniteSum.Group	1154	1155	+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

---

Declarations diff (regex)

+ HasProd.div₀
+ HasProd.inv₀
+ Multipliable.div₀
+ Multipliable.inv₀
+ Multipliable.tprod_div₀
+ Multipliable.tprod_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 3c6d1ff).

• +6 new declarations
• −0 removed declarations

+HasProd.div₀
+HasProd.inv₀
+Multipliable.div₀
+Multipliable.inv₀
+Multipliable.tprod_div₀
+Multipliable.tprod_inv₀

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 3c6d1ffe9e
Reference commit c026161a58

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.

[scholzhannah]

Thank you for your PR! I have left two superficial comments but I don't know anything about this area so I'll unassign myself.

[j-loreaux]

Can you please add the associated lemmas for Multipliable and tprod?

[ajirving]

-awaiting-author

I've added Multipliable and tprod variants.

[j-loreaux]

bors d+

[j-loreaux]

Instead of omitting this everywhere, just out that variable in its own section for the results above.

[mathlib-bors]

✌️ ajirving can now approve this pull request until 2026-08-06 02:36 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.