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r-irber-irbe/proof-skills/skills/lean-pedagogical-exposition/SKILL.md

lean-pedagogical-exposition

Skill3 starsChanged 24 days agoApache-2.0View on GitHub

USE FOR: translating Lean 4 formal proofs into human-readable textbook-grade mathematical descriptions. DO NOT USE FOR: closing open goals in Lean (@lean-proof). TRIGGERS: pedagogical-math, math-exposition, proof-narrative.

The file

We split this skill into the rules it gives an agent

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

  • ≈0

    Common · estimate

    Many files like this have a rule of this kind.

  • ≈0

    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. Very specific:

    Format Blueprint Block: Write the LaTeX snippet with \begin{theorem}[Name] \label{...} \lean{...} \uses{...} \leanok ...

    line 42
  2. Very specific:

    If an informal translation appears weaker or stronger than the formal Lean signature, re-check the exact binder and hypothesis types via …

    line 47
  3. Very specific:

    If dependency extraction is incomplete because .ilean artifacts are missing, run a targeted build via @lean-build first.

    line 51

≈ “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-pedagogical-exposition

Protocol for translating Lean 4 formalizations into clear, beautiful, textbook-quality mathematical exposition, interactive Lean Blueprint chapters, and pedagogical learning materials.

Routing

  • USE FOR:
    • De-formalizing Lean 4 definitions and theorems into intuitive, elegant standard mathematical prose.
    • Converting proof scripts (towers of have, calc, obtain, rcases) into structured narrative proofs with clear motivation.
    • Authoring Lean Blueprint LaTeX chapters with \begin{theorem}, \uses, \lean, \leanok, and informal proof sketches.
    • Designing pedagogical diagrams, flowcharts, and intuition pumps for complex formal proofs.
    • Producing learning zettels and concept cards for the knowledge garden.
  • DO NOT USE FOR:

Workflow

  1. Select Landmark: Identify target theorem or definition from @lean-formalization-breakdown.
  2. Extract Dependencies: Query lean-lsp-mcp or dep_graph.sh to obtain the transitive premise set.
  3. Draft Math Formulation: Translate Lean types and hypotheses into standard mathematical notation ($L^2$, $H^s$, $\nabla \times u$).
  4. Decompose Proof Skeleton: Identify the major intermediate lemmas (have milestones) and draft the narrative proof.
  5. Format Blueprint Block: Write the LaTeX snippet with \begin{theorem}[Name] \label{...} \lean{...} \uses{...} \leanok ... \end{theorem}.
  6. Synthesize Zettel: Emit permanent concept note or reference zettel for the knowledge garden.

Recovery & STOP

  • If an informal translation appears weaker or stronger than the formal Lean signature, re-check the exact binder and hypothesis types via @lean-proof-review before publishing the exposition.
  • If dependency extraction is incomplete because .ilean artifacts are missing, run a targeted build via @lean-build first.

Handoffs

  • Predecessors: skill:lean-formalization-breakdown, skill:lean-blueprint
  • Successors: skill:lean-zettelkasten (saving to knowledge graph), skill:lean-doc-improvement (documentation polishing).
  • Reference Catalog: references/lean_to_math_exposition_patterns.md

Detailed reference

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

See also

  • ../../references/lean-pedagogical-exposition-handbook.md

    Complete lean-pedagogical-exposition Handbook
  • ../lean-gateway/SKILL.md -- Top-level skill router

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