Lists multiple specific concrete actions: 'prove a theorem, lemma, proposition, or corollary', 'fill in missing proof steps', 'formalize a proof sketch', and 'determine whether a claimed proof can actually be completed under the stated assumptions'. These are distinct, well-defined tasks.

Clearly answers both 'what' (writes rigorous mathematical proofs for ML/AI theory) and 'when' with an explicit 'Use when...' clause listing multiple specific trigger scenarios.

Excellent coverage of natural trigger terms including 'prove a theorem', 'lemma', 'proposition', 'corollary', 'proof steps', 'proof sketch', and even Chinese-language equivalents ('补全证明', '写证明', '证明某个命题'). These are terms users would naturally use when requesting proof assistance.

Highly distinctive — scoped specifically to mathematical proofs in the ML/AI theory domain, with very specific trigger terms like 'prove a theorem', 'formalize a proof sketch', and 'fill in missing proof steps'. Unlikely to conflict with general math, coding, or writing skills.

The skill is reasonably well-structured but contains some redundancy (e.g., the extraction checklist in Step 1 and Step 2 overlap significantly, and some instructions like 'never write math in plain text' are repeated implicitly). Several points explain things Claude already knows about proof methodology, though the domain-specific constraints (e.g., never use 'clearly' or 'obviously') add genuine value.

The skill provides highly concrete, specific guidance: exact file structure template, explicit status categories, detailed checklists for verification, specific banned phrases, and clear output format. While there's no executable code (appropriate for a proof-writing skill), every instruction is actionable and unambiguous.

The 6-step workflow is clearly sequenced with explicit validation checkpoints (Step 3 feasibility triage before writing, Step 6 final verification with specific checks). The feedback loop is present: if a step can't be justified, downgrade status and write a blockage report instead. The three output modes handle all possible outcomes clearly.

The content is well-organized with clear sections and headers, but it's a long monolithic document with no references to supporting files. The detailed file structure template, output modes, and key rules could potentially be split into separate reference files. However, given no bundle files exist, the inline approach is somewhat justified.