Lean Verification

Verifying Lean work

A green build establishes exactly one thing: every proof in the library typechecks against its own statement. It does not establish that the statements say what anyone intended, that a theorem is non-vacuous, that a sorry is absent, or that the result matches its description. Those fail independently, and each needs its own check.

The stance that finds defects is "what would have to be true for this to be wrong, and can I show it isn't?", not "does this look right?". Claims here need the output that backs them, because the failure is silent: a wrong "verified" reads exactly like a right one, and gets believed.

The ladder

Each rung is cheap relative to the one above, and a failure below makes everything above it meaningless.

| Rung | Question | Where | |---|---|---| | 1 | Does it build? | references/evidence-ladder.md | | 2 | Is it sorry-free and axiom-clean? | references/evidence-ladder.md | | 3 | Do the linters and the project's own gates pass? | references/evidence-ladder.md | | 4 | Does each statement mean what it claims? | references/soundness-audit.md | | 5 | Is it non-vacuous: does anything satisfy the hypotheses? | references/soundness-audit.md | | 6 | Does the prose match? | the lean-latex-sync skill | | 7 | Has it been formalized before? | references/prior-art.md | | 8 | Does it meet the stated criteria? | references/acceptance-criteria.md |

A project that already has a verify script (.claude/verify/, a scripts/verify.sh, a Makefile target, a repo-local skill) has encoded which surfaces count, and that list is hard-won. Run it, then do the semantic rungs it cannot.

Rungs 1 to 3, in four commands

lake build
grep -rn "\bsorry\b\|\badmit\b\|\bstop\b\|sorryAx" --include="*.lean" YourLib/
lake exe runLinter YourLib        # if Batteries is a dependency

#print axioms myTheorem
-- expect: 'myTheorem' depends on axioms: [propext, Classical.choice, Quot.sound]

#print axioms is the sharpest single check available, because it reports what a proof actually depends on transitively. A sorry anywhere in the dependency chain surfaces as sorryAx, however deep it is buried. Anything else in the list is either a declared project axiom or a hole.

Three ways a green build still proves nothing

Worth holding in mind before reading any "verified" claim, including your own:

• sorry in an example. Lean never adds an example to the environment,

so an environment sweep cannot see one, and a sorry inside it leaves any declaration count unchanged. Only a source-level scan catches these. Treat inline examples as regressions, not as audited declarations.

• Junk-true statements. a / b = c is provable at b = 0 because division

by zero returns 0. The theorem is true and says nothing. See references/soundness-audit.md.

• Vacuous hypotheses. A hypothesis bundle nothing satisfies makes every

conclusion provable. Nothing in the build detects this; only a witness does.

Reporting

State the rung reached, the command, and the output. A finding quotes both sides, the claim and the source it is checked against, because a finding the reader cannot check is one they have to take on trust.

CHECKED   lake build            → exit 0, 0 errors, 0 warnings
CHECKED   sorry scan            → 0 hits across 34 files
CHECKED   #print axioms main_thm → propext, Classical.choice, Quot.sound
FINDING   MyLib/Rates.lean:88 — `ratio_eq` is junk-true at `d = 0` (division
          convention); the docstring claims it holds "for any divisor"
NOT RUN   runLinter — Batteries not in this project's dependencies

NOT RUN is a real and useful line. Omitting a check silently is how a verification report becomes misleading without containing a false sentence.

Sibling skills: lean-proving to fix what this finds, lean-latex-sync for the prose-versus-statement rung, and lake when the build itself is the problem.

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: matt-w-horn
• Source: matt-w-horn/lean-skills
• License: Apache-2.0

Install and usage instructions live in the source repository linked above.