chore(Algebra/BigOperators): add to_additive for expectation and antidiagonal lemmas

[attilavjda]

• Add @[to_additive] attributes to:

  • Expect.expect_inv_index
  • Nat.prod_antidiagonal_succ
  • Nat.prod_antidiagonal_succ'

• Remove the duplicated additive proofs:

  • expect_neg_index
  • sum_antidiagonal_succ
  • sum_antidiagonal_succ'

Used Aristotle AI to find the duplicates, and verify the change, and ChatGPT, AmazonQ to navigate VS Code, cli, running tests, making the PR, understanding the proof and so forth

---

[github-actions]

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[github-actions]

PR summary dce2e44302

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

- expect_neg_index
- sum_antidiagonal_succ
- sum_antidiagonal_succ'

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 dce2e44).

• +0 new declarations
• −0 removed declarations

No declaration differences.

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit dce2e44302
Reference commit 4d476f6d44

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).

[themathqueen]

looks fine to me, thanks!

maintainer merge

[github-actions]

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

[attilavjda]

thank you!