Once ''m'' is fully-acked, ''u'' knows that everyone else has seen ''m'' and all messages before it. We'll call the process of gaining that knowledge, "reaching consistencyfor ''m''"(given context, ''m'' might be implicit). We don't have another mechanism for it, so henceforth we'll use "reach consistency" interchangeably with "reach full-ack", though strictly the former is a security property and the latter is a mechanism for achieving it.