[Merged by Bors] - feat: variations of Submodule.disjoint_map with weaker hypotheses

[ADedecker]

---

[ADedecker]

This one is maybe overkill (and I don't need it), but I had fun figuring out the proof without picking elements.

[tb65536]

Doesn't hker simplify with inf_sup_left to something like f.ker ≤ p ⊓ q or something?

[ADedecker]

p ⊓ q is trivial thanks to hpq, so I assume you mean f.ker ≤ p ⊔ q ? In any case, the point is that the lattice of submodules is not distributive, so inf_sup_left does not apply (for a counterexample you can take three different lines in the plane), and what I'm asking is precisely that the kernel "distributes well" on p ⊔ q. In fact I should probably be able to weaken it a bit more.

[tb65536]

Ah, of course.

[ADedecker]

This sent me into a rabbit hole about lattice theory, which you can follow at https://leanprover.zulipchat.com/#narrow/channel/116395-maths/topic/A.20conjecture.20about.20modular.20lattices/near/609407757. I'll just remove this statement for now, I'll add it together with the required abstract nonsense.

[github-actions]

PR summary b90eaaf837

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ disjoint_map_of_ker_le_left
+ disjoint_map_of_ker_le_right

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 b90eaaf).

• +2 new declarations
• −0 removed declarations

+Submodule.disjoint_map_of_ker_le_left
+Submodule.disjoint_map_of_ker_le_right

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit b90eaaf837
Reference commit 8df0e1b604

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).

[sgouezel]

bors r+
Thanks!

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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• ci (staging) / Build
• ci (staging) / Post-CI job
• ci (staging) / Test and lint