sorryfreeLast reviewed 2026-09-13

Lean 4 and Mathlib

Direct answerLean 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.
Maintainer
Lean FRO and the Mathlib community
Website
https://lean-lang.org
Category
Proof assistants and general verifiers
Targets
CleanzkLeanHalvaArkLibsp1-leanLampeEvmYulCairo AIR proofs
Approach
Interactive theorem prover with a small trusted kernel, a large mathematics library and a growing AI-prover ecosystem
Access
Open source (Apache-2.0)
Status (2026-09-13)
Active

What Lean 4 and Mathlib does

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.

Where it is strong

  • De facto standard for ZK proofs.
  • Mathlib depth for field and polynomial arithmetic.
  • Best AI-assistant support of any prover.

Limits and caveats

  • Proof engineering cost.
  • Fast-moving toolchain; pin versions.
  • Trusted axioms must be audited per project.

When to choose it

Default choice for any new circuit or proof-system verification.

Who works with Lean 4 and Mathlib

zkSecurity, Galois, Nethermind (Formal Verification team), Reilabs.

Top-listed for proof engineering work: zkSecurity
Listed first for the depth of its public formal verification work: the only firm on this index maintaining a circuit framework whose default deliverable is both soundness and completeness (Clean), with verified Keccak, SHA-256, BLAKE3 and Poseidon gadgets, a zkVM verification substrate adopted by Succinct, two live proof-checked challenge platforms, and a published hands-on comparison of the competing frameworks.
Read the zkSecurity profile · Website

Rocq (formerly Coq), Isabelle/HOL, F*, ACL2 (R1CS and PFCS books), K framework and KEVM, Certora Prover.

Sources