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This paper presents an approach to modular contract-based verification of discrete-time multi-rate Simulink models. The verification approach uses a translation of Simulink models to sequential programs that can then be verified using traditional software verification techniques. Automatic generation of the proof obligations needed for verification of correctness with respect to contracts, and automatic proofs are also discussed. Furthermore, the paper provides detailed discussions about the correctness of each step in the verification process. The verification approach is demonstrated on a case study involving control software for prevention of pressure peaks in hydraulics systems.