Lean Tautology Triage

lean-tautology-triage

This skill is a focused review mode for statements that elaborate but may not prove the claim the name, surrounding text, or paper anchor suggests. It does not declare a theorem bad merely because the proof is short; it classifies why a short proof is acceptable or why it needs renaming, strengthening, quarantine, or removal.

Routing

• USE FOR: triaging Lean 4 theorem statements or proof sites that may be vacuous, tautological, smoke-test-only, reflexive-by-rfl, : True placeholders, bare decide closures, or automation-only proofs of supposedly substantive claims.
• DO NOT USE FOR: ordinary proof writing (use @lean-proof); whole-project QA lifecycle (use @lean-quality-engine); running one enforcement script without interpretation (use @lean-enforcement); theorem search (use @lean-research).
• TRIGGERS: tautology, vacuous, trivial proof, smoke theorem, placeholder theorem, proof quality, : True, by decide, by rfl, rfl self-projection, suspicious automation, non-triviality audit.

Workflow

1. Locate the claim [discover] — capture theorem name, statement, proof body, surrounding docstring, imports, and downstream uses. A claim with downstream uses is not automatically substantive, but the use sites explain risk.
2. Classify statement content [validate] — use:
   • VALID-CONTENT: theorem states the intended mathematical/program property.
   • VALID-SMOKE: theorem intentionally checks elaboration or examples only.
   • VACUOUS: theorem is true because hypotheses are impossible or conclusion is True.
   • MISALIGNED: theorem is true but the name/docstring overclaims.
   • UNVERIFIED: statement may be content-bearing but lacks evidence.
   • SUSPECT-FALSE: likely mathematically false or contradicted by examples.
3. Classify proof-quality risk [validate] — use LOW, MEDIUM, HIGH, or DEFINITE. : True placeholders and named smoke tests with theorem-like names are usually DEFINITE; bare decide or rfl on substantive names is HIGH until statement review explains it.
4. Run static support [execute] — use scripts/lean/proof_quality.py for candidate discovery, then manually inspect each P1/P2 result. The script is a triage helper, not a final verdict.
5. Choose remediation [persist] — recommend one of: keep as smoke and rename, restate/strengthen, replace with a real theorem, quarantine as research-only, delete/retire, or ask HITL.

Triage record

## Tautology triage: <decl>

- Location:
- Statement summary:
- Proof shape:
- Downstream uses:
- Statement class:
- Proof-quality risk:
- Evidence:
- Recommended remediation:
- Confidence:
- HITL needed:

Recovery & STOP

• STOP if the statement could be SUSPECT-FALSE or UNVERIFIED and confidence is below the repo belief floor; ask before recommending keep/delete.
• STOP before deleting or weakening a public theorem without an explicit edit claim and rollback path.
• STOP if static proof_quality.py output conflicts with manual inspection; cite both and ask which risk posture to use.
• STOP if a proof is short because of a verified definitional theorem in Mathlib; hand off to @lean-research before labeling it vacuous.

Handoffs

• Predecessors: @lean-proof-review for proof-site review, @lean-quality-engine for project-level quality gates, @lean-enforcement for script execution.
• Successors: @lean-proof-review for final review, @lean-research for theorem/source lookup, @lean-quality-engine for gate rollups.
• Script: scripts/lean/proof_quality.py surfaces candidates; reviewers own final classification.