Lax Lean Archive

While this submission is a draft, it cannot be used by other submissions.

Proof of `Well-defined channel contractions on projected tensor spaces` (2nd statement)

groundedproofs/Lax342547Proofs/TensorContractions.lean · lax-342547

What this proof establishes

no assumptions

lem✓Lax342547.TensorContractions (2nd statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

Description

The chosen ambient extensions agree with their original maps on the two factor spaces, so their outer-product contraction is the required dot product.