Formally Correct

Lean 4 · Mathlib · Machine-checked

Making correctness provable.

We turn short, self-contained papers in mathematics and theoretical computer science into Lean 4 proofs that a computer checks line by line. Human-led, AI-assisted, and delivered with a build you can rerun yourself.

Request a quote See our work

Today: focused papers in mathematics and theoretical computer science. Next: algorithms, protocols and software.

delivery check
$ lake build
✔ Build completed successfully.

$ grep -rn "sorry" Paper/ | wc -l
0

#print axioms Paper.main_theorem
'Paper.main_theorem' depends on axioms:
[propext, Classical.choice, Quot.sound]

∎ Lean's three standard axioms. Nothing else.
1,313theorems proved on prove2.me, each first to be solved
10,845theorem statements published to the prove2.me library
2graduate textbooks formalized, main results of every chapter
129,000lines in our Analytic Combinatorics library, on standard axioms only

What we do

∀

Feasibility assessment

We read your paper, check what Mathlib already covers, find the hardest lemma, and tell you whether a full formalization is realistic, how long it should take, and what it will cost. Fixed fee, quoted up front.

⊢

Paper formalization

Your main theorems stated and proved in Lean 4 with Mathlib. Delivered as a buildable repository with a pinned toolchain, an axiom report, and notes on every place the formal proof differs from the paper.

≟

Statement review

A proof is only as good as its statement. We check by hand that each Lean statement says what the paper says: no missing hypotheses, no vacuous premises, no theorem that is true for the wrong reason.

λ

Refactoring & cleanup

Already have Lean code? We audit it, remove sorry and stray axioms, upgrade it to a current Mathlib, and restructure it so others can read and extend it.

Correctness proofs for algorithms and distributed protocols are available case by case. We have formalized population-protocol results, including the convergence-time bound for approximate majority (Angluin–Aspnes–Eisenstat, 2008).

Track record

Public, buildable, and open to inspection. Numbers below are those stated in each repository.

Analytic Combinatorics

Flajolet & Sedgewick

All nine chapters of the standard reference, including the Hardy–Ramanujan asymptotic for the partition function proved without the circle method, singularity analysis, Lagrange inversion and Pólya theory.

  • 419 Lean files
  • ~129,000 lines
  • 622 audited theorems
  • standard axioms only
Repository link available on request

An Invitation to q-Series

Hei-Chi Chan, 2011

The pentagonal number theorem, Jacobi triple product, Rogers–Ramanujan identities, Ramanujan's congruences modulo 5, 7 and 11, and a tenth-order mock theta identity. Every chapter's main result is checked by Lean.

  • 258,052 lines
  • 174 files
  • ~27,600 theorems & lemmas
Repository link available on request

Silent self-stabilizing exact majority

SSS 2025

Correctness and space optimality of the Kanaya et al. population protocol, with the impossibility result for protocols that do not know n. Zero sorry, standard axioms.

Repository link available on request

Fast robust approximate majority

Distrib. Comput. 2008

A high-probability O(n log n) convergence-time bound for the three-state protocol of Angluin, Aspnes and Eisenstat.

Repository link available on request

Stanley–Wilf growth limits

Combinatorics

The unconditional growth-limit theorem for permutation classes, via Marcus–Tardos and the symbolic method, built on our analytic combinatorics library.

Repository link available on request

prove2.me

Open theorem library

As FormallyCorrect on the open Lean platform prove2.me, we have led nine formalization missions, published 10,845 theorem statements, and been first to prove 1,313 of them.

prove2.me →

How a project runs

  1. 1

    Send us the paper

    Email the PDF (or arXiv link), the theorems you care about, and your deadline. Initial screening is free and takes about one business day.

  2. 2

    Paid assessment

    Within a fixed time box we read the proofs, map dependencies against Mathlib, and prototype the riskiest step. You receive a written report: proceed, major gap, refuted, or inconclusive.

  3. 3

    Quote & statement of work

    A written quote naming the exact theorems, the Lean and Mathlib versions, milestones, the acceptance test, and a cost ceiling. Nothing beyond it is billed without your approval.

  4. 4

    Formalization

    Work proceeds in milestones with status reports at agreed dates: on track, at risk, or blocked. No "90% done" progress bars.

  5. 5

    Verified delivery

    You see the build and the axiom report before final payment. After settlement we hand over the full repository.

  6. 6

    Invoice & receipt

    Formal invoices and paid receipts suitable for grant accounting and reimbursement.

What "verified" means

  • It builds. A pinned lean-toolchain and lake-manifest.json, so lake build reproduces our result on your machine.
  • No holes. Zero sorry, zero custom axioms. We report the output of #print axioms for every headline theorem.
  • The right statement. Each formal statement is reviewed by a person against the paper, with differences written down.
  • Readable. Organized by section of your paper, so a referee can find the proof of Lemma 3.2 without a guide.

When a paper has a gap

Formalization is unforgiving, and sometimes it finds real problems. We formalize; we do not rewrite your mathematics. If we hit a substantial error or gap, we stop, deliver a written report locating it as precisely as we can, and charge only for the work done under the agreed stage. Unused prepayment is refunded.

A proof we cannot formalize is not the same as a false theorem. We say which one we found, and we say what we did not check.

Pricing

Quoted by hand

Papers differ too much for a price list. A short combinatorics argument on well-supported Mathlib ground is a different job from a paper that needs new library infrastructure. Every project gets an individual quote after assessment, with a hard cost ceiling.

Pay in stages

The assessment is billed up front and credited toward the project if you go ahead. Larger projects are split into milestones, each paid on acceptance.

Institutional billing

Card and ACH through Stripe. Universities may pay by purchase order on Net 30 terms. A W-9 and formal invoice are available on request.

Confidentiality & AI

We use AI tools, including commercial models from Anthropic and OpenAI, under human direction. Every result is checked by Lean, not by a language model. If you send unpublished work, relevant parts may be processed by these providers under their terms; where a provider offers it, we use settings that exclude your material from model training. We never publish your material or use it as a showcase without written permission. If your work cannot leave your hands, tell us before sending it, and we will tell you what we can and cannot offer.

Request a quote

We are a small, new practice. Every message is read and answered by a person, usually within two business days.

Helpful to include:

  • The paper (PDF or arXiv link) and the theorems you want formalized
  • Your deadline, and whether it is firm
  • Any existing Lean code, and the Lean/Mathlib version you need
  • Whether the work is unpublished or confidential
  • How you will pay: personally, grant, or university purchase order