Triple parabolic cosets have unique Bruhat minima

A folklore result says that any parabolic double coset $W_{I} w W_{J}$ in a Coxeter group $W$ is an interval of the Bruhat order, provided that $W_{I}$ and $W_{J}$ are finite. We include a self-contained proof, without assuming that $W$ is finite. Furthermore, we prove that each "triple coset" $W_{I