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For safe navigation in dynamic uncertain environments, robotic systems rely on the perception and prediction of other agents. Particularly, in occluded areas where cameras and LiDAR give no data, the robot must be able to reason about potential movements of invisible dynamic agents. This work presents a provably safe motion planning scheme for real-time navigation in an a priori unmapped environment, where occluded dynamic agents are present. Safety guarantees are provided based on reachability analysis. Forward reachable sets associated with potential occluded agents, such as pedestrians, are computed and incorporated into planning. An iterative optimization-based planner is presented that alternates between two optimizations: nonlinear Model Predictive Control (NMPC) and collision avoidance. Recursive feasibility of the MPC is guaranteed by introducing a terminal stopping constraint. The effectiveness of the proposed algorithm is demonstrated through simulation studies and hardware experiments with a TurtleBot robot. The paper is available at https://arxiv.org/abs/2211.09156