Proposition: Relay-gap stability

If two implemented relay laws are respectively within ${\eta }_{0,n},{\eta }_{1,n}$ of ${\delta }_0,{\delta }_1$, then

A sum of local half-diamond errors bounds each ${\eta }_{b,n}$.

Proof. Use the triangle inequality and $d_{\mathrm{TV}}({\delta }_0,{\delta }_1)=1$. The second statement follows from Lemma lem:telescope and terminal readout contraction.