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proof-readability

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Improve the exposition and readability of a mathematical proof already verified as correct without changing its mathematics. Use when polishing a lemma, theorem, proof, or appendix after correctness checks. Not for verifying the proof; use $verify-math.

skills/proof-readability/SKILL.md

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> **Author:** Moran Koren, Ben-Gurion University of the Negev (korenmor@bgu.ac.il). Part of the [Theorist Toolbox](https://github.com/morankor/theorist-toolbox).

# Proof readability

> **Relationship to `proofread`:** `proofread` is a *report-only*, whole-paper prose checker (11 categories, never edits source). `proof-readability` *edits in place*, is proof-specific, runs only after a correctness gate, and holds a content-preservation invariant `proofread` does not. Audit a whole paper's prose → `proofread`; edit the exposition of a verified proof → `proof-readability`.

Edit verified proofs so a reader can follow them without reconstructing steps, chasing broken references, or decoding notation. This skill runs *after* a proof has been written (e.g., by `math-proof`) and *after* its correctness has been verified (by `domain-reviewer`, `lean-check`, or the user). It is an exposition pass, not a proving pass.

## Position in the pipeline

```
math-proof  →  verification (domain-reviewer / lean-check / user)  →  proof-readability
   (correctness)              (acceptance)                  (exposition only)
```
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