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Found 5 Skills
Verify, check, transform, and repair Lean 4 proofs using the Axiom (Axle) CLI and API. Supports proof verification, syntax checking, theorem extraction, code transformation (rename, merge, simplify), proof repair, and disproving. Use this skill whenever the user works with Lean 4 code, formal mathematics, Mathlib theorems, or mentions axiom, axle, lean verify, proof verification, formal proof, or theorem checking -- even if they don't explicitly say "axiom" but are clearly working with Lean proofs that need machine verification.
Use when editing .lean files, debugging Lean 4 builds (type mismatch, sorry, failed to synthesize instance, axiom warnings, lake build errors), searching mathlib for lemmas, formalizing mathematics in Lean, or learning Lean 4 concepts. Also trigger when the user asks for help with Lean 4, mathlib, or lakefile. Do NOT trigger for Coq/Rocq, Agda, Isabelle, HOL4, Mizar, Idris, Megalodon, or other non-Lean theorem provers.
Writes and reviews structured Lean 4 proofs and designs Lean libraries following Mathlib conventions. Use when proving theorems in Lean, formalizing mathematics or specifications in Lean 4, defining new types or definitions in a Lean library, reviewing Lean proofs for readability and maintainability, refactoring long tactic proofs into lemmas, filling in sorry placeholders in a Lean development, setting up CI or linters for a Lean project, diagnosing slow proofs or maxHeartbeats timeouts, or writing custom tactics, macros, or linters.
Search Mathlib for lemmas by type signature pattern
Formal theorem proving with research, testing, and verification phases