Manuscript Oai069-A@1 · Oai069-A.tex · proposition · a4913aab

Proposition: Conditional transfer, with a named norm

The exact remaining source-to-operation bridge · lines 1650–1668 · proof included or linked

Oai069-A@1#prop:transfer

Suppose a bridge provides channels on the same declared finite input and output algebras, and

d_{⋄} (Φ_{source}, Φ_{benchmark}) \leq b_{1}, d_{⋄} (Φ_{benchmark}, T) \leq b_{2} .

Then

d_{⋄} (Φ_{source}, T) \leq min {1, b_{1} + b_{2}} .

All reference comparisons are retained.

Proof. Apply the triangle inequality for the complete channel norm.

Displayed formulas in this passage

unlabeled · line 1654
$d_{⋄} (Φ_{source}, Φ_{benchmark}) \leq b_{1}, d_{⋄} (Φ_{benchmark}, T) \leq b_{2} .$
unlabeled · line 1660
$d_{⋄} (Φ_{source}, T) \leq min {1, b_{1} + b_{2}} .$