Proof of `Dimension and component-rank bounds for effective test spaces` (2nd statement)
groundedproofs/Lax342547Proofs/EffectiveBounds.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 generating outer product is in the image of the canonical linear map from S tensor T to matrices. Its range dimension is bounded by the dimension of the domain, which is the product of the two dimensions.