Safety assessment of new air traffic management systems is a main issue for civil aviation authorities. Standard techniques such as testing and simulation have serious limitations in new systems that are significantly more autonomous than the older ones. In this paper, we present an innovative approach for establishing the correctness of conflict detection systems. Fundamental to our approach is the concept of trajectory, and how we represent a continuous physical trajectory by a continuous path in the x-y plane constrained by physical laws and operational requirements. From the model of trajectories, we extract, and formally prove, high-level properties that can serve as a framework to analyze conflict scenarios. We use the AILS (Airborne Information for Lateral Spacing) alerting algorithm as a case study of our approach.