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Lean specification

Skill r-irbe/proof-skills/skills/lean-specification

APM-installable agent skills for Lean 4 and Mathlib4 — proof tactics, math domains, review and research workflows, generic tooling.

Install
npx -y skills add r-irbe/proof-skills --skill lean-specification

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USE FOR: Design theorem specifications for Lean 4 proofs. Use when planning new theorems, lemmas, definitions, or tactics. Covers the three-part specification (requirements, design, documentation), lifecycle management, dependency analysis, and integration with the review council. DO NOT USE FOR: actual proof writing (use @lean-proof); requirement extraction (use @lean-doc-requirements); review (use @lean-proof-review). TRIGGERS: specification, theorem spec, three-part spec, lemma plan, tactic plan.

SKILL.md

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Lean 4 Theorem Specification

Structured process for specifying theorems before implementation. Every theorem passes through Specify → Design → Implement → Review → Merge, with each stage tracked by document templates.

Routing

  • USE FOR: Design theorem specifications for Lean 4 proofs. Use when planning new theorems, lemmas, definitions, or tactics. Covers the three-part specification (requirements, design, documentation), lifecycle management, dependency analysis, and integration with the review council.
  • DO NOT USE FOR: actual proof writing (use @lean-proof); requirement extraction (use @lean-doc-requirements); review (use @lean-proof-review).
  • TRIGGERS: specification, theorem spec, three-part spec, lemma plan, tactic plan.

Workflow

  1. Identify the artifact: new theorem, new lemma, new definition, or new tactic.
  2. Apply the three-part specification template from the body (signature, intent, traceability); verify Mathlib primitives exist at the pin.
  3. Produce the spec; add explicit non-goals + dependencies.
  4. Hand off: to @lean-proof for the proof, to @lean-proof-review once proven, to @lean-zettelkasten.

Recovery & STOP

  • STOP if the artifact is informal — extract requirements via @lean-doc-requirements first.
  • STOP if the spec depends on Mathlib primitives missing at the pin — escalate to @lean-research.
  • STOP if reviewer would reject on grounds the body covers (vacuous truth, missing hypothesis) — fix before publishing.

Handoffs

  • Predecessors: agent:gateway, skill:lean-research.
  • Successors: skill:lean-proof, skill:lean-proof-review, skill:lean-zettelkasten.

Detailed reference

Full content for lean-specification lives in references/lean-specification-handbook.md. Load that file when the skill is convened; the SKILL.md only carries the dispatch contract and the parts index.

(See handbook for full content.)

See also

Gives 0 of the 12 instructions most docs writing skills give

Counted across 1,637 of the 3,044 authors here whose files we hold, read 2026-08-06

  • announce the skill at startin 54 of 1637, across 21 files
  • convert legacy doc files before editingin 45 of 1637, across 7 files
  • predict questions readers might askin 42 of 1637, across 3 files
  • Generate clarifying questions for initial contextin 42 of 1637, across 3 files
  • Create document scaffold with placeholder textin 42 of 1637, across 3 files
  • Brainstorm content options for each sectionin 42 of 1637, across 3 files
  • Test document with fresh context-less instancein 42 of 1637, across 3 files
  • ask interview questions one at a timein 42 of 1637, across 26 files
  • include exact file paths in every taskin 42 of 1637, across 15 files
  • Apply surgical edits during refinementin 41 of 1637, across 2 files
  • Offer structured workflow or freeformin 40 of 1637, across 1 file
  • Ask for document meta-contextin 40 of 1637, across 1 file

Said here and by no other author read

  • Apply the three-part specification template
  • Verify Mathlib primitives exist at the pin
  • Add explicit non-goals and dependencies
  • Hand off artifacts to the appropriate successor skill
  • Load the detailed handbook reference

Grouped from the skills themselves: near-identical wordings counted once, and counted by distinct author, so one author publishing three of these counts once.

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