Proof of `Exact-image bounds for independent affine columns` (1st statement)
groundedproofs/Lax342547Proofs/AffineImages.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 failure of column injectivity has a nonzero coefficient relation. For each relation, its single image is uniform on an affine space whose translation dimension is at least dim(S). Union over at most 2^|J| coefficient vectors gives the stated bound.