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In this paper, we integrate an assertion-based verification methodology with our object-oriented system-level synthesis methodology to address the problem of HW/SW co-verification. In this direction a system-level assertion language is defined. The system-level assertions can be used to monitor the current state of system or flow of transactions. These assertions are automatically converted to ''monitor hardware'' or ''monitor software'' during the system-level synthesis process depending on their type and also synthesis style of their corresponding functions. The synthesized assertions are functionally equivalent to their original system-level assertions, and hence, can be reused to verify the system after HW/SW synthesis and also at run-time after system manufacturing. This way, not only system-level assertions are reused in lower-levels of abstraction, but also run-time verification of system is provided. In this paper, we describe the system-level assertion language and explain the corresponding synthesis method in our object-oriented system-level synthesis methodology; however the concept can be applied to any system-level design methodology with modifications to assertion types and synthesis method.