feat(Data/Nat/Choose/Multinomial): add positivity support

[BoltonBailey]

This PR adds positivity tactic support for Multiset.multinomial, by adding a _pos theorem and an extension.

This was done as a part of Project Numina's LeanTriathlon project. AI was used as an assistant in the creation of this PR.

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[github-actions]

PR summary 0a7aa2ff62

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)

+ multinomial_pos

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 0a7aa2f).

• +2 new declarations
• −0 removed declarations

+Multiset.evalMultinomial
+Multiset.multinomial_pos

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 0a7aa2ff62
Reference commit 4608056c77

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).

[joneugster]

Thank you for the PR!

[joneugster]

maintainer delegate

since the comments are all about better style, nothing conceptual.

[github-actions]

🚀 Pull request has been placed on the maintainer queue by joneugster.

[BoltonBailey]

Seems I had to update it just now for the new positivity extension format, but I didn't change much.

[joneugster]

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by joneugster.