proof-writer

Provide the exact theorem statement, assumptions, notation, and any proof sketch you have. The skill normalizes the claim, builds a dependency map of lemmas and cited theorems, then writes a numbered proof with justification for every nontrivial step in a structured proof package file.

The skill performs feasibility triage before writing: it verifies the conclusion follows from the listed assumptions, checks cited theorems are used within their conditions, and looks for counterexamples or quantifier failures. If unjustified, it reports the blockage instead of fabricating a proof.

The skill never silently strengthens assumptions or narrows scope. It either proposes an explicitly weakened claim with a full proof, or issues a blockage report with a counterexample or repaired statement, preserving your original theorem statement throughout.

Yes. Point to your existing proof file, theorem notes, or appendix drafts, and the skill reads them first, updates the relevant claim section, and fills gaps without duplicating prior content. It defaults to writing in PROOF_PACKAGE.md unless you specify another target.

The skill produces rigorous human-readable proofs, not machine-checked formalizations like Lean or Coq. Genuinely open problems will receive a blockage report rather than a proof, and any remaining fragile points are listed explicitly under Open Risks.