Proof of `Poincaré–Birkhoff–Witt for Lie polynomials`
groundedproofs/Lax825748Proofs/PBW.lean · lax-825748
What this proof establishes
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Shuffle pairings separate the ordered monomials. Reordering adjacent basis elements changes a product only by terms of lower Lie degree, which proves spanning by induction on that degree.