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In this paper, we investigate the axiomatic system of Modeling Simulation and Verification Language (MSVL). To this end, a set of state axioms and state inference rules is given. They are useful to deduce a program into its normal form. Further, a propositional projection temporal logic is used as assertion language to describe the required property of a program. Moreover, to deduce a program over an interval, a set of rules in terms of triple like Hoare logic is formalized. These rules enable us to deduce a program in its normal form at the current state to the next one and to verify safety, liveness properties over an interval.