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r-irber-irbe/proof-skills/skills/lean-specification/SKILL.md

lean-specification

Skill3 starsChanged 24 days agoApache-2.0View on GitHub

USE FOR: Design theorem specifications for Lean 4 proofs. DO NOT USE FOR: actual proof writing (@lean-proof). TRIGGERS: specification, theorem spec, three-part spec, lemma plan.

The file

We split this skill into the rules it gives an agent

5 rules. About 0 are common, 2 are distinctive, and 3 are very specific to this project.

  • ≈0

    Common · estimate

    Many files like this have a rule of this kind.

  • ≈2

    Distinctive · estimate

    This author's own choices. Worth a look.

  • 3

    Very specific

    Tied to their project's names, files or tools. Probably skip.

  • Common
  • Distinctive
  • Very specific
  1. Distinctive:

    Run mandatory specification fidelity checks before approving:

    line 43
  2. Very specific:

    Check 5 (Necessity & Sufficiency ↔ Pairing): Every executable Bool checker

    line 44
  3. Very specific:

    STOP if the artifact is informal — extract requirements via @lean-doc-requirements first.

    line 51
  4. Very specific:

    STOP if the spec depends on Mathlib primitives missing at the pin — escalate to @lean-research.

    line 52
  5. Distinctive:

    STOP if reviewer would reject on grounds the body covers (vacuous truth, missing hypothesis) — fix before publishing.

    line 53

≈ “Common” is an estimate: at least 1 in 5 of the 350,495 skill files we read have a rule of the same kind, not the same words. “Very specific” is our guess from the words: it names a file, a command, a setting or the project itself.

Keep what fits and drop the rest. Your version, ready for your agents.
Files
SKILL.md

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. Run mandatory specification fidelity checks before approving:
    • Check 5 (Necessity & Sufficiency ↔ Pairing): Every executable Bool checker f ... : Bool or decidable predicate MUST specify both soundness and completeness (f x = true ↔ Spec x), never a one-way f x = true -> ... implication alone (ONE_WAY_BOOL_CHECKER).

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 encyclopedic reference, decision trees, and lookup tables live in references/lean-specification-handbook.md .

See also

  • ../../references/lean-specification-handbook.md -- Complete lean-specification Handbook
  • ../lean-gateway/SKILL.md -- Top-level skill router

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