Proof of `Finite linear images and their uniform-law density bounds` (4th statement)
groundedproofs/Lax342547Proofs/FiniteLinearLaw.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
Every nonempty fiber is a translate of the kernel. Binary vector spaces have 2^dimension elements, so rank-nullity bounds the fiber density by 2^c. Divide the cardinal inequality by the positive uniform denominators.