feat(Data/ENNReal/Inv): add ENNReal.div_mul_div_cancel

[jdhart81]

Proves a / b * (b / c) = a / c for b ≠ 0, b ≠ ∞ in ENNReal. Proof via mul_div_assoc and existing div_mul_cancel.

AI Disclosure: This PR was developed with assistance from an LLM (Claude, Anthropic) for proof exploration and text drafting. The proof was compiled and verified locally by the contributor, who understands the mathematical content. This lemma is extracted from a larger formalization of information-theoretic bounds (Zenodo DOI: 10.5281/zenodo.19317983).

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[github-actions]

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[github-actions]

PR summary fcdf55d904

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff (regex)

++ div_mul_div_cancel

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 fcdf55d).

• +2 new declarations
• −0 removed declarations

+ENNReal.div_mul_div_cancel
+EReal.div_mul_div_cancel

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit fcdf55d904
Reference commit 9eb53bdd74

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).

[felixpernegger]

Good to have; I'm surprised this is still missing (but in fact actually is, according to loogle).

While you are at it, can you also add the corresponding lemma in EReal?

[felixpernegger]

awaiting-author

[jdhart81]

Thanks @felixpernegger — yes, I’ll add the corresponding EReal.div_mul_div_cancel lemma and reword the ENNReal docstring so it doesn’t describe b as a shared denominator. I’ll push both updates together.

[jdhart81]

Implemented both review requests in dd84ea8:

• Reworded the ENNReal docstring to describe cancellation of the finite nonzero middle term.
• Added the corresponding EReal.div_mul_div_cancel lemma.

Both changed modules compile locally with the pinned mathlib toolchain.

-awaiting-author

[jdhart81]

CI note: the fresh fork workflow is failing before it reaches the changed files. Both red jobs stop in the cache restore step with uncaught exception: leantar not found in Lean sysroot under Lean v4.29.0-rc1. The style/lint checks pass, and I locally rebuilt Mathlib.Data.ENNReal.Inv and Mathlib.Data.EReal.Inv successfully at dd84ea8283. I left the source unchanged; fork contributors cannot rerun the upstream workflow without repository admin permission.

[felixpernegger]

The costrings are still not ideal. Can you just delete both docstrings? (The correspodning lemma for groups also is not documented, so this should be fine)

[felixpernegger]

@jdhart81 try to merge Master on github, this probably solves the issue

[jdhart81]

Done — I merged current master and removed both docstrings. The refreshed CI suite is green.