Proof of `Conditional independence of the two channel frames` (1st statement)
groundedproofs/Lax342547Proofs/ConditionalChannels.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
The zero-Gram fibers are precisely the independent uniform columns in the two annihilators. Their failure to extend P and Q injectively is bounded by 2^(2d+h-N) on each side, before the separate rank conditionings.