Proof of `Exact images mixing independent injective frames` (3rd statement)
groundedproofs/Lax342547Proofs/ProductImages.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 a basis of the nominal coefficient image and lift it through the coefficient map. Right multiplication by its lift extracts a full-rank tuple of exactly the original nominal rank from any tested tuple.