google-deepmind / google-deepmind/formal-conjectures
OEIS/211417: `formal_proof` anchor points at the form without `0 < D`
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- Lean
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Description
`OEIS/211417.lean`, `general_divisibility`:
```lean
theorem general_divisibility (r : ℕ) (hr : 1 ≤ r) :
∃ D : ℤ, 0 < D ∧ ∀ n : ℕ, (divisorProduct n r) ∣ (D * (a n : ℤ))
```
The `formal_proof` attribute anchors line 651 of the linked file. The declaration at that line is
```lean
theorem general_divisibility (r : ℕ) (hr : 1 ≤ r) :
∃ D : ℤ, ∀ n : ℕ, (divisorProduct n r) ∣ (D * (a n : ℤ))
```
without `0 < D`. The same file proves `general_divisibility_is_vacuous` with `D = 0`, and separately proves the statement that matches main as `general_divisibility_strong` (witness `Dwit r = (r!)^(r*r)` with `Dwit_pos`).
The docstring in main says the permalink "proves the non-vacuous form". The mathematics is there; the anchor is on the weak form.
Suggested fix: point the link at `general_divisibility_strong`. Happy to open the PR if that is the preferred route.
Found by fetching every `formal_proof` target and comparing the statement at the anchor with the statement in main (script to follow as a PR).
Contributor guide
Research direction
Inspect OEIS/211417.lean around general_divisibility, general_divisibility_strong, and the formal_proof anchor referenced by the main docstring. Update the link to general_divisibility_strong, then verify that the permalinked declaration includes 0 < D and matches the non-vacuous statement described in main.
Written by the indexing model from the issue text.
Assessment
- Domain
- documentation
- Issue type
- Documentation
- Difficulty
- 1/5
- Estimated time
- Under an hour
- Activity status
- Active
- Clarity
- Clearly specified
- Newbie friendliness
- 90/100