Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx agentmods add commands/cbirkbeck/mathlib-quality/decompose-proofgit clone --depth 1 https://github.com/CBirkbeck/mathlib-qualityWhat 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 | $0.00011 | $0.05527 |
| Opus 5 | $0.00005 | $0.02763 |
| Sonnet 5 | $0.00002 | $0.01105 |
| Haiku 4.5 | $0.00001 | $0.00553 |
Grade A, and why
decompose-proof 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 2d 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.
How it starts
The opening of the file, as written. The whole thing — 587 lines — stays where its author put it; the contents beside it link to each section on GitHub.
/decompose-proof - Two-Pass Proof Decomposition
CRITICAL: No proof should exceed 50 lines. Target: main theorems <15 lines.
Break long proofs into helper lemmas by understanding the mathematical structure first, then implementing.
Usage
/decompose-proof [file_path]
/decompose-proof [theorem_name]
If no argument, operates on the currently open file.
Architecture
Problem: Agents rush into decomposition without fully understanding the proof. They miss mathlib lemmas, create single-use helpers with bad names, and forget to consolidate.
Solution: Separate analysis from implementation:
- Pass 1 (Analysis): Identify ALL proofs needing decomposition. For each, study the mathematics and write a detailed decomposition plan as a comment block above the proof.
- Pass 2 (Decompose): Dispatch parallel agents, each handling one proof. They study the proof, search mathlib, then implement the plan.
- Pass 3 (Consolidate): Review all new helpers for duplicates and shared patterns.
Pass 1: Analysis
Step 1: Identify Candidates
Read the entire file and build a table of ALL proofs by length:
## Proof Length Report
| Declaration | Lines | Action |
|-------------|-------|--------|
| `main_theorem` | 65 | CRITICAL (>50) — aggressive decomposition |
| `helper_result` | 38 | MUST decompose (>30) |
| `medium_proof` | 22 | CONSIDER decomposition (15-30) |
| `small_lemma` | 12 | OK |
Also flag structural issues regardless of length:
∧in theorem statement → MUST splitconstructorwith any branch >10 lines → MUST extract branchesby_cases/rcases/match/inductionwith any branch >10 lines → MUST extract branchesset_option maxHeartbeats→ MUST decompose (remove the set_option)
Step 2: Study Each Candidate
For EACH proof flagged for decomposition, read it carefully before writing any plan. Answer these questions (write answers in your reasoning, not in the file):
- What is the theorem proving? (plain language, 1-2 sentences)
- What are the key mathematical steps? (3-5 bullet points, using math language like "establish bound", "show convergence", NOT "apply lemma X")
- What independent facts are being established? (each is a candidate helper)
- What estimates/bounds appear? (
have h : ‖...‖ ≤ ...blocks are extraction candidates) - Are there cases/branches >10 lines? (mandatory extraction)
- Are there repeated patterns across proofs? (consolidation candidates)
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.
- 2d ago First seen · 587 lines · 11 tokens per session scan A 60d3ff87a85c
decompose-proof is a command published in the GitHub repository CBirkbeck/mathlib-quality (32 stars, last pushed 13d ago), licensed MIT. It adds 11 tokens to every session and 5,527 once invoked, about $0.0001 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.
Other commands, from other repositories
checklist
Generate a custom checklist for the current feature based on user requirements.
clarify
Identify underspecified areas in the current feature spec by asking up to 5 highly targeted clarification questions and encoding answers back into the spec.
specify
Create or update the feature specification from a natural language feature description.
analyze
Perform a non-destructive cross-artifact consistency and quality analysis across spec.md, plan.md, and tasks.md after task generation.
converge
Assess the current codebase against the feature's spec, plan, and tasks, then append any remaining unbuilt work as new tasks to tasks.md so implement can complete it.
implement
Execute the implementation plan by processing and executing all tasks defined in tasks.md.