Location-dependent services are services that adapt their behavior based on the locations of mobile devices. For many applications, it is critical that location-dependent services use trustworthy device locations, namely locations that are both accurate and recent. These properties are captured by a security goal called locale authentication whereby an entity can authenticate the physical location of a device, even in the presence of malicious adversaries. In this paper, we present a systematic technique for verifying that location discovery protocols satisfy this security goal. We base our work on the strand space theory which provides a framework for determining which security goals a cryptographic protocol achieves. We extend this theory with a metric that captures the geometric properties of time and space. We use the extended theory to prove that several prominent location discovery protocols including GPS do not satisfy the locale authentication goal. We also analyze a location discovery protocol that does satisfy the goal under some reasonable assumptions.