Scan the whole repository for over-engineering — a ranked list of what to delete, simplify, or replace with stdlib/native equivalents. Read-only; applies no fixes.
USE FOR: bisecting Lean 4 toolchain versions or commits to find which one introduced a regression, using `script/lean-bisect` with `#guard_msgs` / exit-code signatures, ignoring…
USE FOR: generating Lean blueprint, annotating theorems with @[blueprint], scaffolding blueprint directory, building blueprint LaTeX, rendering blueprint web.
Build, test, and debug Lean 4 projects using Lake. Use when building the ComputationalPaths project, checking for errors, running tests, cleaning artifacts, or debugging Lean 4…
Generate a Lean Canvas with problem, solution, metrics, cost structure, UVP, unfair advantage, channels, segments, and revenue.
USE FOR: Formalize causal DAGs, knowledge graph quality gates, counterfactual reasoning, and provenance bridges in Lean 4.
Collaborative theorem proving orchestrator. Uses lc CLI for state, spawns parallel agents.
Restructure agent-facing docs so the always-loaded context stays small and the rest is loaded on demand.
Context Runtime for AI Agents — 48 MCP tools, 10 read modes, 90+ shell patterns, tree-sitter AST for 18 languages. Compresses LLM context by up to 99%.
USE FOR: reviewing a Lean documentation draft, flagging undefined terms, suggesting cross-links, scoring readability against a rubric.
USE FOR: Update academic papers, technical reports, and documentation based on results from Lean 4 formalization.
USE FOR: Extract formal requirements from academic papers, technical reports, and design documents. Use when converting informal mathematical claims into Lean 4 theorem…
Agent-legible documentation setup and auditing for any codebase. Use whenever the user asks to set up docs, audit docs, create or slim down CLAUDE.md, organise documentation,…
Diagnose and improve Lean 4 elaboration performance in a repo — locate genuine hot spots, route by profile phase, apply the proven levers (consumer import narrowing, nlinarith…
Run a repeatable elaboration test of ONE Lean 4 repo and write a dated report — snapshot size (date, commit, lines excluding comment-only files), clean project-only rebuild with…
USE FOR: running programmatic CI / pre-review / post-review gates for a Lean 4 project — axiom audit, council precheck, review coverage, metric sync, zettelkasten lint, bridge…
Use when preparing optional LeanExplore MCP setup for Lean declaration search and formalization support.
Use for Lean 4 and Mathlib — lake, the LSP goal loop, lemma search, tactics, soundness.
Lean 4 fundamentals including syntax, structures, inductive types, and polymorphism. Use when writing basic Lean code, defining custom data types, pattern matching, or learning…
Combining multiple effects with monad transformers including StateT, ExceptT, ReaderT, and OptionT. Use when you need error handling AND state, or multiple effects together.
Ad-hoc polymorphism and operator overloading in Lean. Use when defining type classes, creating instances, implementing interfaces, deriving, or working with coercions.
Use when Lean 4 proofs involve fuel-based recursion, proving fuel independence, loop invariants, copyLoop-style patterns, suffix/append extension lemmas, or…
USE FOR: routing the top-level entry-point for a complex Lean 4 task; selecting which downstream skill(s) own each phase; preventing context collapse across long sessions;…
Guides adding new Higher Inductive Types to the ComputationalPaths library. Use when creating new HITs, defining fundamental group (pi1) calculations, implementing encode-decode…
USE FOR: Cross-skill integration protocol defining how all 39 skills work together. Covers the complete lifecycle from document to proof to document, inter-cluster communication,…
USE FOR: Knowledge representation, ontology engineering, symbolic AI, commonsense reasoning, causal reasoning, legal reasoning, and abductive inference in Lean 4.
Reusable Lean 4 and Mathlib lessons for analysis formalizations. Use when choosing an ambient carrier or repository layout, debugging elaboration and typeclass costs, preserving…
When the user wants to implement lean principles, eliminate waste, improve flow, or adopt continuous improvement.
Compress routine agent responses to reduce token usage while preserving commands, file paths, assumptions, risks, verification details, and next actions.
USE FOR: creating minimal working examples (MWEs) from Lean 4 errors for upstream bug reports, capturing diagnostics with `#guard_msgs`, capturing panics with `#guard_panic`,…
Use when naming Lean declarations, organizing files, adding docstrings, or cleaning code so it matches Mathlib conventions and review expectations.
USE FOR: Formalize and extend nested learning theory in Lean 4. Covers LaSalle invariance, hierarchical learners, multi-scale Lyapunov functions, timescale separation, and bridges…
Use when choosing implementation patterns for observability, runtime configuration, API typing, CI, auth, or infrastructure.
Coordinate a large multi-agent Lean 4 formalization around exact author-approved declarations, source-level dependency graphs, independent statement audits, bounded proof tasks,…
Reduce output tokens while preserving technical accuracy. Trigger: When asked to be concise, terse, or minimize token usage.
USE FOR: opening, titling, or labelling a PR against any Lean ecosystem repo (`leanprover/lean4`, `leanprover-community/mathlib4`, Cslib, or downstream projects), picking the…
Viết PRD rút gọn tập trung Business Rules và Workflow cho AI-first engineering + BDD. Use when user wants to write a lean PRD, viết PRD, tạo spec, feature spec, business rules,…
Use when planning a Lean formalization, selecting and freezing author-approved declarations, choosing module boundaries, designing reusable APIs, or staging a large proof project…
Use whenever a user wants to set up AI coding assistant instructions for their project. Triggers: "add a CLAUDE.md", "set up Copilot instructions", "configure Cursor rules",…
USE FOR: writing Lean 4 proofs one tactic at a time, fixing tactic errors by priority, planning sorry placeholders, cleaning a working proof, resolving dependent-type rewriting…
Use when writing, refactoring, or debugging Lean proofs and you need a stable translation from mathematical reasoning into explicit tactics, controlled rewriting, or maintainable…
USE FOR: reviewing one Lean 4 proof / file for correctness, soundness, statement faithfulness, non-triviality, and proof quality; running the 4-layer verification checklist…
GF(3)-balanced random walk through Lean proof states. Use when generating formal proof chains with parallel triad verification.
A skill for using Lean 4, a modern interactive theorem prover with powerful type theory, dependent types, and mathematical structures.
Prepare and verify a private Lean repository for public release. Use for source scrubbing, selective syncs, clean history, proof-status and license review, fresh-checkout builds,…
USE FOR: assessing overall Lean 4 project quality across seven dimensions (soundness, faithfulness, completeness, novelty, elegance, integration, documentation); preparing for…
Consolidated cheatsheets for Lean 4 syntax, tactics, type classes, monads, and common patterns. Use for quick lookup or when you need a reminder.
USE FOR: converting a Lean 4 project blueprint into a publication-grade LaTeX report — blueprint artifact ingestion (extracted LaTeX nodes, dependency DAG, JSON metadata),…
USE FOR: running a Lean 4 corpus retrospective — RETRO protocol (Refactor-Extract-Test-Refine-Optimize), adapting to project scale (Solo / Small / Medium / Large), per-phase…
USE FOR: Apply the review council system retroactively to an existing large Lean 4 project. Use when onboarding an existing codebase to the council review framework.
Review the current diff for over-engineering only — what to delete, reuse, or simplify. One line per finding; never edits files.
USE FOR: orchestrating a 5-member Lean 4 proof review council (Σ Kernel Guardian, Φ Statement Oracle, Ν Novelty Scout, Λ Quality Architect, Ω Integration Sentinel); running RALPH…
Use when proving encode/decode roundtrip theorems, suffix invariance (_append lemmas), goR (decode-with-remaining) patterns, padding extraction, or composing per-level roundtrip…
Use when searching Mathlib for existing declarations, likely theorem names, relevant files, or proof ingredients before attempting a new Lean proof.
USE FOR: bootstrapping a fresh leanprover/lean4 clone, repairing elan toolchains, linking stage0/stage1 builds, verifying that `lean` and `lake env lean` agree, cleaning up linked…
USE FOR: Design theorem specifications for Lean 4 proofs. Use when planning new theorems, lemmas, definitions, or tactics.
Design MVPs, validated learning experiments, and pivot-or-persevere decisions using Build-Measure-Learn.
Applied lean startup methodology covering build-measure-learn loops, MVP design, pivot decisions, validated learning, innovation accounting, and practical techniques for reducing…
Provides startup advice using Eric Ries' Lean Startup methodology focusing on Build-Measure-Learn cycles, validated learning, and rapid experimentation.
精益创业（Lean Startup）的结构化思维工具。基于 Eric Ries、Steve Blank、Ash Maurya 等一手来源的深度调研， 提炼 5 个核心原理和完整的操作协议。 触发词：「精益创业」「lean startup」「MVP」「验证假设」「最小可行产品」「pivot」「转型」。