Proof of `Orthogonality and finite Walsh correlation bounds` (4th statement)
groundedproofs/Lax342547Proofs/Walsh.lean · lax-342547
What this proof establishes
no assumptions
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
Absorb each subprobability mass into its bounded weight. Its squared energy is at most its point-mass cap times its total mass, hence at most the cap. The squared Walsh bound and a square root give Lemma 4.6(b).