Most recent studies on establishing intersection safety focus on the situation where all vehicles are fully autonomous. However, currently most vehicles are human-driven and so we will need to transition through regimes featuring a varying proportion of human-driven vehicles ranging from 100% to 0% before realizing such a fully autonomous future - if ever. We will, therefore, need to address the safety of hybrid systems featuring an arbitrary mixture of human-driven and autonomous vehicles. In fact, recent incidents involving autonomous vehicles have already highlighted the need to study the safety of autonomous vehicles co-existing with human-driven vehicles. Motivated by this we address the design of provably safe intersection management for mixed traffic consisting of a mix of human-driven vehicles (HVs) as well as autonomous vehicles (AVs). To analyze such mixed traffic, we model HVs as near-sighted and with relatively loose constraints, permitting worst-case behavior while AVs are considered capable of following much tighter constraints. HVs are allowed freedom to change their speed at any time while AVs are only allowed to change their speed at the beginning of a time slot through a Model Predictive Controller (MPC). AVs are assumed to possess a shorter response time and stronger braking capability than HVs in collision avoidance. Moreover, AVs obtain the permissions of passing through the intersection through vehicle-to-infrastructure (V2I) communication, while HVs achieve the same objective by following traffic lights. Taking the above differences into consideration, we propose a provably safe intersection management for mixed traffic comprised of an MPC-based protocol for AVs, a permission assignment policy for AVs along with a coordination protocol for traffic lights. In order to respect the distinctiveness of HVs, the proposed protocol ensures that the traffic lights, as well as the semantic meanings of their colors, are consistent with current practice. A formal proof of safety of the system under the proposed combined protocol is provided.