Proof of `Uniform injective frames and channel transpose failure` (4th statement)
groundedproofs/Lax342547Proofs/InjectiveFrames.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
Before injectivity conditioning, transpose evaluation is a uniform h-by-q matrix, whose column-rank failure is at most 2^(q-h). Conditioning the channel frame itself to be injective multiplies this by at most two.