---
id: CVE-2026-72844
title: >-
  The Lean 4 kernel does not verify that the structure named in a projection
  expression matches the type of the value being projected, and
  environment::add_inductive in src/kernel/inductive.cpp did not type check the
  nested inductive appli…
summary: >-
  The Lean 4 kernel does not verify that the structure named in a projection
  expression matches the type of the value being projected, and
  environment::add_inductive in src/kernel/inductive.cpp did not type check the
  nested inductive appli…
severity: medium
cvss: 6.3
cvssVector: 'CVSS:3.1/AV:L/AC:L/PR:N/UI:R/S:C/C:N/I:H/A:N'
cwe:
  - CWE-843
published: '2026-08-20'
updated: '2026-09-24'
sourceUpdated: '2026-09-24T20:43:32.537'
source: NVD
sourceUrl: 'https://nvd.nist.gov/vuln/detail/CVE-2026-72844'
references:
  - url: 'https://github.com/endrazine/lean-cve-poc'
    label: disclosure@vulncheck.com
  - url: 'https://github.com/leanprover/lean4'
    label: disclosure@vulncheck.com
  - url: >-
      https://github.com/leanprover/lean4/commit/a39eab69e1eee9ad38f4efe507907b1026a77808
    label: disclosure@vulncheck.com
  - url: 'https://github.com/leanprover/lean4/issues/14576'
    label: disclosure@vulncheck.com
  - url: 'https://github.com/leanprover/lean4/pull/14577'
    label: disclosure@vulncheck.com
  - url: 'https://github.com/xrchz/CollatzLean'
    label: disclosure@vulncheck.com
  - url: 'https://www.openwall.com/lists/oss-security/2026/08/02/1'
    label: disclosure@vulncheck.com
  - url: >-
      https://www.vulncheck.com/advisories/lean-4-kernel-type-checking-bypass-via-mismatched-structure-projections
    label: disclosure@vulncheck.com
tags:
  - nvd
  - exploit-available
epss: 0.00176
epssPercentile: 0.06379
exploits:
  github: 1
  githubRepos:
    - 'https://github.com/endrazine/lean-cve-poc'
  checkedAt: '2026-09-26T09:05:58.382Z'
exploitAvailable: true
ingestedAt: '2026-09-24T20:51:40.212Z'
---

## Overview

The Lean 4 kernel does not verify that the structure named in a projection expression matches the type of the value being projected, and environment::add_inductive in src/kernel/inductive.cpp did not type check the nested inductive applications that are replaced by auxiliary types, so their parametric arguments escaped checking. A metaprogram running in the Lean process can register an ill-typed nested inductive whose constructor applies a .proj C 0 projection to a value of the unrelated type W, and the kernel admits the declaration through the ordinary checked addDecl path at maximum kernel checking, without sorry, unsafeCast, debug.skipKernelTC, addDeclWithoutChecking, FFI, or a modified .olean file. The result is a type confusion yielding a proof of False that carries no axioms, from which any proposition can be derived. The published proof of concept additionally pads two expressions until their hashes and approximate depths collide, which defeats kernel caching; that is the technique used to reach the flaw, not its cause. Exploitation requires running a metaprogram in-process, for example by building a project or importing a malicious Lake dependency.

## Remediation

Refer to the linked advisories for vendor-supplied fixes and affected version ranges.