Proof of `Gram-conditioned columns and their rank-failure probability` (1st statement)
groundedproofs/Lax342547Proofs/GramColumns.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
Translate the fixed Gram fiber into a product of plus-annihilator spaces. The affine-column dependence bound and rank-nullity give 2^(p+q-N), with no restriction on the Gram values.