feat(Counterexamples): an invertible semimodule of different cardinality than the semiring

[alreadydone]

example due to Sixuan Gu (CUHKSZ) and Wei Qi (Ohio State U)

---

[github-actions]

PR summary 7c1f8915ed

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ M₆
+ M₆_eq_finset
+ R₇
+ add
+ cardinalMk_M₆
+ cardinalMk_R₇
+ c₁
+ c₂
+ gc₁_eq_ac₂
+ gc₂_eq_bc₁
+ instance : Add R₇ where add := add
+ instance : CommSemiring R₇
+ instance : Module.Invertible R₇ M₆ := .left linearEquiv
+ instance : Nontrivial (CommRing.Pic R₇)
+ instance : Zero R₇ where zero := zero
+ instance [Finite R] : Finite (MaximalSpectrum R)
+ linearEquiv
+ linearMap
+ mul
+ not_cardinalMk_eq_of_moduleInvertible
+ not_subsingleton_Pic_of_finite
+ not_subsingleton_Pic_of_finite_maximalSpectrum
+ span_c₁_c₂
+ Θ

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 7c1f891).

• +1 new declarations
• −0 removed declarations

+MaximalSpectrum.instFinite

---

Increase in strong tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (strong)
4928	1	backward.isDefEq.respectTransparency

No changes to weak technical debt.

Current commit 7c1f8915ed
Reference commit b4a18d6453

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).