FormalProofLinter.lean`

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Annotation provenance. This overlay contains 10 curated AI-written annotations and 7190 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

9 declarations, 3 contain sorry, 0 declared as axioms

Imports (1)

FormalConjecturesUtil.Linters.FormalProofLinter

theorem FormalProofLinter.an_open_assumption An assumption that is still open, which is the ordinary case sorry line 27 source
Source documentation
An assumption that is still open, which is the ordinary case.

depends on sorry (Lean reported 2 error(s) in this file) what this means
Statement uses: Eq, Nat, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem an_open_assumption : 0 = 0 := by
…
```
theorem FormalProofLinter.conditional_on_an_open_assumption line 35 source
theorem FormalProofLinter.a_proved_assumption An assumption that has since been proved line 39 source
Source documentation
An assumption that has since been proved.
```
theorem a_proved_assumption : 2 = 2 := by
…
```
theorem FormalProofLinter.conditional_on_a_proved_assumption line 52 source
theorem a_formal_proof_with_sorry sorry line 61 source
depends on sorry (Lean reported 2 error(s) in this file) what this means
Statement uses: Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem a_formal_proof_with_rfl line 73 source
theorem a_formal_proof_with_partial_proof sorry line 85 source
depends on sorry (Lean reported 2 error(s) in this file) what this means
Statement uses: Nat, Eq
Proof uses: Nat.casesAuxOn, OfNat.ofNat, sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, Eq.symm, HAdd.hAdd, Eq.refl
4 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
theorem mixed_conditional_and_unconditional_proofs line 99 source
theorem multiple_conditional_proofs line 114 source