CtrlK
BlogDocsLog inGet started
Tessl Logo

lemma-discovery-assistant

Analyze failed or stuck proofs and propose auxiliary lemmas to help complete the proof in Isabelle/HOL or Coq. Use when encountering proof failures, stuck proof states, unprovable subgoals, or when needing to strengthen induction hypotheses. Identifies missing lemmas, suggests proof strategies, and generates helper lemmas with appropriate statements and proof sketches. Supports inductive proofs, case analysis, rewriting, and complex proof obligations.

88

1.13x
Quality

83%

Does it follow best practices?

Impact

93%

1.13x

Average score across 3 eval scenarios

SecuritybySnyk

Passed

No findings from the security scan

SKILL.md
Quality
Evals
Security

Quality

Content

67%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 content is well-structured with genuinely executable, complete proof examples and sensible one-level-deep references, but it runs long and restates conceptual material Claude already knows. Tightening the taxonomic and troubleshooting prose would improve token efficiency without losing actionability.

Suggestions

Trim the 'Common Symptoms', 'Questions to ask', and gap-type taxonomy lists, which restate obvious proof-failure signals Claude can infer from the error message and proof state.

Move the full worked 'Complete Lemma Discovery' insertion-sort example (or the per-pattern stuck/usage triples) into references/proof_patterns.md, keeping only one compact illustration inline.

Replace the abstract Step 1-2 prose ('What to look for', 'Questions to ask') with the concrete diagnostic actions already shown in the examples, or fold them into a short checklist.

DimensionReasoningScore

Conciseness

The body is mostly efficient with valuable concrete code, but padded with conceptual restating Claude already knows (Common Symptoms, Questions to ask, gap-type taxonomies, Best Practices, Troubleshooting) that could be trimmed.

3 / 5

Actionability

Provides executable, complete Isabelle/Coq code with full proofs covering inductive, generalization, rewrite, and structural patterns, though the discovery-process steps themselves remain partly abstract.

4 / 5

Workflow Clarity

The five-step Lemma Discovery Process is clearly sequenced and a Troubleshooting section exists; this is not a destructive/batch operation so the validation cap does not apply, but explicit checkpoints are implied rather than enforced.

4 / 5

Progressive Disclosure

References to isabelle_lemmas.md, coq_lemmas.md, and proof_patterns.md are well-signaled and point to real files, but the main body inlines many full worked examples that could live in those references.

4 / 5

Total

15

/

20

Passed

Description

100%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.

The description is precise, third-person, and explicitly pairs capabilities with concrete usage triggers for a well-scoped theorem-proving niche. It is a strong model description with no notable gaps.

DimensionReasoningScore

Specificity

Lists multiple concrete actions (analyze failed proofs, propose auxiliary lemmas, identify missing lemmas, suggest strategies, generate helper lemmas with proof sketches) and enumerates supported proof types, giving comprehensive coverage.

5 / 5

Completeness

Explicitly answers 'what' (analyze/propose/identify/suggest/generate) and 'when' via a concrete 'Use when encountering...' clause with multiple trigger conditions.

5 / 5

Trigger Term Quality

Includes natural phrases a theorem-prover user would actually say ('failed or stuck proofs', 'proof failures', 'stuck proof states', 'unprovable subgoals', 'strengthen induction hypotheses') with several synonyms, matching the comprehensive anchor.

5 / 5

Distinctiveness Conflict Risk

Occupies a clear niche (auxiliary lemma discovery in Isabelle/HOL and Coq) with distinctive proof-failure triggers and minimal overlap with other skills.

5 / 5

Total

20

/

20

Passed

Validation

100%

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

Validation16 / 16 Passed

Validation for skill structure

No warnings or errors.

Repository
ArabelaTso/Skills-4-SE
Reviewed

Table of Contents

Is this your skill?

If you maintain this skill, you can claim it as your own. Once claimed, you can manage eval scenarios, bundle related skills, attach documentation or rules, and ensure cross-agent compatibility.