{
  "slug": "lean4",
  "name": "Lean 4 and Mathlib",
  "tagline": "The proof assistant the ZK verification ecosystem has standardised on",
  "maintainer": "Lean FRO and the Mathlib community",
  "url": "https://lean-lang.org",
  "category": "provers",
  "targets": [
    "Clean",
    "zkLean",
    "Halva",
    "ArkLib",
    "sp1-lean",
    "Lampe",
    "EvmYul",
    "Cairo AIR proofs"
  ],
  "approach": "Interactive theorem prover with a small trusted kernel, a large mathematics library and a growing AI-prover ecosystem",
  "license": "Open source (Apache-2.0)",
  "status": "Active",
  "summary": "Lean 4 is the proof assistant behind nearly every ZK verification project funded in 2025 and 2026: Clean, zkLean, Halva, ArkLib, sp1-lean, Lampe, proven-zk, Nethermind's EVM model and StarkWare's Cairo proofs. Mathlib supplies the finite-field and polynomial mathematics, and AI proving tools now target it.",
  "details": [
    "Choosing Lean fixes the hiring pool, the reusable libraries and the interoperability with everything else on this index. The kernel is small; the axioms a project uses (and whether it relies on `native_decide`) are the things to check when reading a Lean result, which is why zk.golf enforces an axiom allowlist."
  ],
  "strengths": [
    "De facto standard for ZK proofs.",
    "Mathlib depth for field and polynomial arithmetic.",
    "Best AI-assistant support of any prover."
  ],
  "limits": [
    "Proof engineering cost.",
    "Fast-moving toolchain; pin versions.",
    "Trusted axioms must be audited per project."
  ],
  "fit": [
    "Default choice for any new circuit or proof-system verification."
  ],
  "references": [
    [
      "Lean",
      "https://lean-lang.org"
    ],
    [
      "Introduction to interactive theorem provers (zkSecurity, 2025-02-04)",
      "https://blog.zksecurity.xyz/posts/introduction-to-interactive-theorem-provers/"
    ]
  ],
  "category_name": "Proof assistants and general verifiers",
  "page": "https://sorryfree.com/frameworks/lean4/",
  "updated": "2026-09-13"
}