Proof of `The row-corank bound for a uniform binary matrix` (1st statement)
groundedproofs/Lax342547Proofs/CorankCounting.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
Choose independent row relations for each bad matrix, and partition by that choice. There are at most 2^(sm) relation matrices. Each fiber has at most 2^((m-s)n) matrices because all n columns lie in a kernel of dimension m-s.