Proof of `Walsh operator bounds with explicit bilinear rank` (3rd statement)
groundedproofs/Lax342547Proofs/BilinearWalsh.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
Group the second weight over the fibers of the matrix's linear map. Fiberwise Cauchy-Schwarz costs at most 2^(number of columns - rank) in squared energy. Apply the full dot-product Walsh bound to the resulting weight on the row-coordinate space.