proof-writer

To write rigorous mathematical proofs for ML theory, this Skill produces a formal PROOF_PACKAGE.md containing a dependency map, explicit assumptions, notation, and a structured proof plan before drafting the exact claim. It automates proof drafting for theorems, lemmas, and propositions.

A formal proof package is a structured document declaring proof status, dependency maps, explicit assumptions, and notation. It is needed when formalizing proof sketches, completing missing steps, or evaluating prove-ability for ML/AI theory claims in academic papers and notes.

Yes, you can fill in missing proof steps and formalize proof sketches by providing the target theorem. The Skill generates complete proofs for exact claims, provides corrected claims with proofs, or delivers blockage reports if the proof cannot be completed under stated assumptions.

Check whether a claimed proof can be completed by providing the statement and its assumptions. The Skill evaluates prove-ability and either completes the proof or generates a blockage report explaining why the claim is not currently justified under the stated assumptions.

Yes, it integrates with local notes and existing theorem drafts to align with project workflows. You provide the target theorem from your existing materials, and the Skill produces the formal proof package while maintaining consistency with your current drafts.

The main limitation is that automation cannot always justify a claim; if assumptions are insufficient, the Skill outputs a blockage report rather than a proof. It focuses on ML/AI theory and requires explicit assumptions and notation to produce checkable results.