Proof of `Bit rank and Walsh bounds for global vector-slot pairings` (2nd statement)
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
The image of the bit matrix is linearly equivalent to N independent copies of the coefficient matrix's image. Dimensions add over that finite product, giving the exact bit rank.