What is extract-lemma?

A command for taking a verified, self-contained part of a semantic proof graph and saving it as a reusable lemma. A proof graph represents claims, assumptions, and their dependencies.

Use it to extract a lemma from a graph, check whether extraction is valid with a dry run, or write the result to another file.

It lets you separate completed proof sections, making them easier to reuse and reducing the amount of context needed later.

How tobiasosborne/alethfeld configures Claude Code

Reuse

Borrowing it

Nothing to install: this file belongs to tobiasosborne/alethfeld. Take a copy, put it at the same path in your own repository, and replace the rules that are about this project with yours.

Copy the file

curl -O https://raw.githubusercontent.com/tobiasosborne/alethfeld/legacy/.claude/commands/extract-lemma.md

Clone the repo

git clone --depth 1 https://github.com/tobiasosborne/alethfeld

Made for: Claude Code.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

README.md

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Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

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Per session 7 Only the description is in the session, so the agent can decide to use it. The body loads when it is invoked.

When invoked 616 The whole file, excluding the scripts and references it only reads on demand.

Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe.

Origin original No closer match found in the catalogue.

Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

Model	Per session	Once invoked
Fable 5.1	$0.00007	$0.00616
Opus 5	$0.00003	$0.00308
Sonnet 5	$0.00001	$0.00123
Haiku 4.5	$0.00001	$0.00062

Measured 10d ago against content hash 1197ae57bcd6, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-10, from the pricing page.

Security

Grade A, and why

extract-lemma scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 10d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

.claude/commands/extract-lemma.md · 86 lines

How it starts

The opening of the file, as written. The whole thing — 86 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Extract Lemma

Extract a verified subgraph as an independent, reusable lemma.

When to Use

Use this command when:

A portion of the proof is complete and self-contained
You want to reduce context window usage
A result is worth extracting for reuse

Invocation

./cli/scripts/alethfeld extract-lemma <graph.edn> <root-node-id> --name "Lemma Name"

Arguments

<graph.edn> - Path to the proof graph
<root-node-id> - The root node of the extraction (e.g., :1-abc123)

Required Options

--name NAME or -n NAME - Name for the lemma (e.g., "L1-fourier")

Optional Options

--nodes IDS or -N IDS - Explicit comma-separated node IDs to extract
- If not provided, extracts root + all ancestors
--dry-run or -d - Validate without writing
--output FILE or -o FILE - Write to different file

Extraction Rules

All nodes must be verified - Only :verified nodes can be extracted
Only root has external dependents - No other internal node can be depended upon from outside
Scope must be balanced - Every :local-assume must have a matching :local-discharge

Examples

Extract with automatic ancestor detection:

./scripts/alethfeld extract-lemma proof.edn :1-abc123 -n L1-fourier

Extract specific nodes:

./scripts/alethfeld extract-lemma proof.edn :1-abc123 -n L2-result -N :1-abc123,:1-def456,:2-ghi789

Dry run to check validity:

./scripts/alethfeld extract-lemma proof.edn :1-abc123 -n Test --dry-run

What Happens

A lemma record is created in :lemmas
A :lemma-ref node replaces the root (same statement)
Extracted nodes are moved to :archived-nodes
External dependents now depend on the lemma-ref
Context budget estimate decreases

Output Format

Success:

{:status :ok
 :message "Lemma L1-fourier extracted with 6 nodes"
 :lemma-id "L1-fourier"
 :nodes-extracted 6
 :graph-version 27}

Error Handling

:not-all-verified - Some nodes are not verified
:external-deps-on-non-root - Internal node has external dependents
:unbalanced-scope - Local assumes not properly discharged

Read the full file on GitHub · 86 lines

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

10d ago First seen · 86 lines · 7 tokens per session scan A 1197ae57bcd6

Subscribe to this mod's changes

extract-lemma is a command published in the GitHub repository tobiasosborne/alethfeld (144 stars, last pushed 3mo ago), licensed MIT. It adds 7 tokens to every session and 616 once invoked, about $0.0000 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.

Scientific

verify-math

Verify a self-authored mathematical result end to end by routing claims across adversarial review, numerical falsification, symbolic or CAS checks, and Lean, then aggregating one report. Use when a theorem, proposition, conjecture, or paper-wide mathematical argument needs the appropriate combination of verification…

flonat/flonat-research · 81 tokens

alethfeld: Command for Claude Code