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Lean specification

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

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.From its SKILL.md

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

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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

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