Safety-critical systems such as spacecraft are typical embedded systems with the characteristics of multi-task concurrency and frequent interruptions. The operating system is the most fundamental software of computer, and building a correct operating system is crucial to ensure the reliability of the spacecraft system. Exception management, as the lowest level function of the operating system, is responsible for guiding sudden changes of control flow in response to certain changes in the processor state. Exception management is the basis for the correctness of the entire operating system correctness. This study proposes a verification framework based on Hoare-logic to prove the correctness of exception management for SPARC processor architecture operating systems. Especially for multi-task concurrency and frequent interruption of real-time operating system exception nesting and task switching in exceptions, the exception management is divided into five stages for comprehensive formal modeling, and this framework is implemented in the Coq proving theorem assistant tool. Based on this framework, the correctness of the exception management function of the spacecraft embedded real-time operating system SpaceOS, which is actually used by China's Beidou-3, is verified.