Proposition: Monotonicity under release

For the specified nested schedule,

Proof. Discarding the additional received cells takes ${{\mathcal{N}}_{k+1}}^U$ to ${{\mathcal{N}}_k}^U$, so an earlier decoder remains an available policy. The later complement is a partial trace of the earlier complement. That partial trace maps replacement channels to replacement channels and maps the named center ${{\sigma }_{B_k}}^U$ to ${{\sigma }_{B_{k+1}}}^U$. Use diamond contraction.