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lean-formalize

Develop and verify a mathematical proof in Lean, continue an incomplete Lean project, or audit whether it proves the original statement. Connect actual inputs to intermediate lemmas, assemble the target theorem, check its transitive axioms, and provide a reproducible handoff. Use when Lean is requested or a specific proof obligation benefits from formal verification; use proof-writer for ordinary mathematical drafting.

Quality

85%

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SKILL.md
Quality
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Quality

Content

73%Weight 40%Scale 1-5

Reviews the quality of instructions and guidance provided to agents. Good implementation is clear, handles edge cases, and produces reliable results.

The body delivers an unusually rigorous, well-sequenced verification workflow with explicit validation checkpoints and genuine Lean-specific failure-mode guidance, and it uses its reference files correctly. Its main costs are length and repetition — routing and cross-family-review rules are restated multiple times, and no concrete build/audit commands are shown inline.

Suggestions

State the reviewer-routing resolution once (either the opening blockquote or the 'Host execution and review' subsection) and point to the shared reference for the rest; the two passages currently repeat the same resolution order and unavailability rules.

Add one or two concrete audit commands (e.g., `lake build <module>` and `#print axioms <theorem>` with sample output) inline or in verification-and-handoff.md, since section 5 mandates printing types and transitive axioms but never shows how.

Merge the repeated cross-family/provisional-review rules (they appear in the core workflow, section 4, and section 5) into a single statement, trimming roughly a page of duplicated caveats.

DimensionReasoningScore

Conciseness

Most lines are dense, high-signal domain policy rather than padding, but the reviewer-routing rules are stated twice (the opening blockquote and the "Host execution and review" subsection) and cross-family/provisional-review caveats recur across sections 4 and 5, so the body could be meaningfully tightened. It is above the noticeably-verbose anchor at 2 because nearly every rule addresses a real Lean-formalization failure mode.

3 / 5

Actionability

Concrete guidance is abundant — entry decision tables, a 7-step implementation loop with specific tactics (`#check` unfamiliar declarations, compile the affected then downstream module, diagnose the first relevant error), an executed-verification checklist, and a continuation-note template. It falls short of fully-executable because no example commands (e.g., `lake build`, `#print axioms <name>`) appear inline; command details are deferred to the reference files.

4 / 5

Workflow Clarity

The workflow is clearly sequenced (numbered sections, core-workflow diagram with A/B/C checkpoints), validation is explicit ("explicitly build the module that proves the target and print its type and transitive axioms"), and the implementation loop embeds a compile→diagnose→repair feedback loop plus an evidence checklist, exactly matching the top anchor.

5 / 5

Progressive Disclosure

Deep operational detail is appropriately pushed to three real, clearly-signaled, one-level-deep references (adversarial-review.md, lean-working-loop.md, verification-and-handoff.md — all verified present), each introduced with when-to-read guidance. It misses the top anchor because the 360-line body itself carries substantial routing/policy prose (e.g., the 16-line reviewer-routing blockquote) that reads as inlined material belonging in the shared references.

4 / 5

Total

16

/

20

Passed

Description

92%Weight 40%Scale 1-5

Based on the skill's description, can an agent find and select it at the right time? Clear, specific descriptions lead to better discovery.

A strong description: concrete, comprehensive, third-person, with an explicit trigger clause and explicit de-confliction from adjacent proof skills. The only weakness is slightly thin natural-synonym coverage for users who would ask to "formalize" a theorem or use "theorem proving" phrasing.

DimensionReasoningScore

Specificity

The description enumerates seven concrete actions spanning all three entry modes ("Develop and verify a mathematical proof in Lean", "continue an incomplete Lean project", "audit whether it proves the original statement", "check its transitive axioms", "provide a reproducible handoff") with no coverage gaps, matching the comprehensive-coverage anchor rather than the minor-gaps anchor at 4.

5 / 5

Completeness

It explicitly answers both what (develop/verify, continue, audit Lean proofs) and when ("Use when Lean is requested or a specific proof obligation benefits from formal verification"), and even adds negative routing guidance ("use proof-writer for ordinary mathematical drafting"), matching the top anchor.

5 / 5

Trigger Term Quality

Natural terms users would say are present ("Lean", "mathematical proof", "formal verification", "proof obligation", "incomplete Lean project"), but common synonyms like "formalize", "theorem proving", or "Lean 4" are missing, so it fits good-but-not-comprehensive keyword coverage rather than the comprehensive-synonyms anchor at 5.

4 / 5

Distinctiveness Conflict Risk

It carves out a clear Lean formal-verification niche and explicitly disambiguates the neighboring skill ("use proof-writer for ordinary mathematical drafting"), giving minimal conflict risk.

5 / 5

Total

19

/

20

Passed

Validation

93%

Checks the skill against the spec for correct structure and formatting. All validation checks must pass before discovery and implementation can be scored.

Validation — 15 / 16 Passed

Validation for skill structure

CriteriaDescriptionResult

relative_links

Relative link issues: 4 suspicious

Warning

Total

15

/

16

Passed

Repository

wanshuiyin/Auto-claude-code-research-in-sleep

Path

skills/skills-codex/lean-formalize/SKILL.md

Reviewed

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