Proof of `Well-defined channel contractions on projected tensor spaces` (3rd statement)
groundedproofs/Lax342547Proofs/TensorContractions.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
Extend the proposed functional linearly to all matrices. Its values on the outer-product generators agree with the constructed contraction, which determines its restriction to their span uniquely.