Show that, during an exponential expansion phase of the universe, the proper distance between any two comoving objects separated by more than H−1 grows at a speed exceeding the speed of light. Hence show that an observer in such a universe can only see processes occurring inside the 'horizon' radius H−1, and so the process of inflation in any spatial domain of radius H−1 (or 'mini-universe') occurs independently of any events outside it.