I’m pretty sure that I covered this before, but I stripped out all the distractions. bondeconomics.com/2019/06/why-sp…
Since the steady state rate of interest depends on policy, we cannot say it constrains it.
Rather than show the property holds in a model, demonstrate that models which violate it are crazy.
(My article is loose, but it would not be hard to tighten up, since the concept is trivial.)