claude-bot
caedf2e6f4
- extract_section.py: slice a book section out of a pdftotext -layout dump and list its labeled Theorem/Proposition/Lemma/Corollary/Definition items. - formalize.py: LLM-formalize a section into Lean 4 candidate statements (preferring Mathlib vocabulary) plus a definitions manifest. - check_statements.py: elaboration-only sanity check against a real Mathlib-backed Lean project (must run outside the Cowork sandbox, which has no Lean toolchain and can't run macOS binaries anyway). - build_library.py: assemble solved lean-bench results into a reusable .lean file, reusing each winning proof verbatim. - llm.py: standalone OpenAI-compatible chat client + .env loader, kept independent of lean_agent so this pipeline works without it installed. - Source PDFs and raw/layout text dumps are gitignored (copyrighted material); only code and the final short Lean statement datasets are tracked.
118 lines
3.2 KiB
JSON
118 lines
3.2 KiB
JSON
[
|
|
{
|
|
"kind": "Proposition",
|
|
"label": "1.6.1",
|
|
"first_line": "Proposition 1.6.1."
|
|
},
|
|
{
|
|
"kind": "Proposition",
|
|
"label": "1.6.2",
|
|
"first_line": "Proposition 1.6.2. Let a, b, c, u, and v denote integers."
|
|
},
|
|
{
|
|
"kind": "Definition",
|
|
"label": "1.6.3",
|
|
"first_line": "Definition 1.6.3. A natural number is prime if it is greater than 1 and not"
|
|
},
|
|
{
|
|
"kind": "Proposition",
|
|
"label": "1.6.4",
|
|
"first_line": "Proposition 1.6.4. Any natural number other than 1 can be written as a"
|
|
},
|
|
{
|
|
"kind": "Theorem",
|
|
"label": "1.6.6",
|
|
"first_line": "Theorem 1.6.6. There are infinitely many prime numbers."
|
|
},
|
|
{
|
|
"kind": "Proposition",
|
|
"label": "1.6.7",
|
|
"first_line": "Proposition 1.6.7. Given integers a and d , with d \u0015 1, there exist unique"
|
|
},
|
|
{
|
|
"kind": "Definition",
|
|
"label": "1.6.8",
|
|
"first_line": "Definition 1.6.8. A natural number d is the greatest common divisor of"
|
|
},
|
|
{
|
|
"kind": "Proposition",
|
|
"label": "1.6.9",
|
|
"first_line": "Proposition 1.6.9. For integers n and m, let"
|
|
},
|
|
{
|
|
"kind": "Lemma",
|
|
"label": "1.6.10",
|
|
"first_line": "Lemma 1.6.10. Let m and n be nonzero integers. If a natural number d"
|
|
},
|
|
{
|
|
"kind": "Proposition",
|
|
"label": "1.6.11",
|
|
"first_line": "Proposition 1.6.11. The natural number nr is the greatest common divisor"
|
|
},
|
|
{
|
|
"kind": "Corollary",
|
|
"label": "1.6.13",
|
|
"first_line": "Corollary 1.6.13. Let m and n be nonzero integers, and write d D"
|
|
},
|
|
{
|
|
"kind": "Definition",
|
|
"label": "1.6.14",
|
|
"first_line": "Definition 1.6.14. Nonzero integers m and n are relatively prime if"
|
|
},
|
|
{
|
|
"kind": "Corollary",
|
|
"label": "1.6.15",
|
|
"first_line": "Corollary 1.6.15. Two nonzero integers m and n are relatively prime if"
|
|
},
|
|
{
|
|
"kind": "Corollary",
|
|
"label": "1.6.17",
|
|
"first_line": "Corollary 1.6.17. Suppose that a and b are relatively prime natural num-"
|
|
},
|
|
{
|
|
"kind": "Proposition",
|
|
"label": "1.6.18",
|
|
"first_line": "Proposition 1.6.18. If p is a prime number and a is any nonzero integer,"
|
|
},
|
|
{
|
|
"kind": "Proposition",
|
|
"label": "1.6.19",
|
|
"first_line": "Proposition 1.6.19. Let p be a prime number, and a and b nonzero inte-"
|
|
},
|
|
{
|
|
"kind": "Corollary",
|
|
"label": "1.6.20",
|
|
"first_line": "Corollary 1.6.20. Suppose that a prime number p divides a product"
|
|
},
|
|
{
|
|
"kind": "Theorem",
|
|
"label": "1.6.21",
|
|
"first_line": "Theorem 1.6.21. The prime factorization of a natural number is unique."
|
|
},
|
|
{
|
|
"kind": "Definition",
|
|
"label": "1.6.22",
|
|
"first_line": "Definition 1.6.22. A natural number d is the greatest common divisor of"
|
|
},
|
|
{
|
|
"kind": "Lemma",
|
|
"label": "1.6.23",
|
|
"first_line": "Lemma 1.6.23. Given nonzero integers a1 ; a2 ; : : : ; an (n \u0015 2), there is a"
|
|
},
|
|
{
|
|
"kind": "Proposition",
|
|
"label": "1.6.24",
|
|
"first_line": "Proposition 1.6.24. The greatest common divisor of nonzero inte-"
|
|
},
|
|
{
|
|
"kind": "Definition",
|
|
"label": "1.6.25",
|
|
"first_line": "Definition 1.6.25. We say that non-zero integers a1 ; : : : ; an are relatively"
|
|
},
|
|
{
|
|
"kind": "Lemma",
|
|
"label": "1.6.26",
|
|
"first_line": "Lemma 1.6.26. Let a1 ; : : : ; an be pairwise relatively prime integers, and"
|
|
}
|
|
]
|