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This paper deals with the problem of safety verification of non-linear hybrid systems. We start from a classical method that uses interval arithmetic to check whether trajectories can move over the boundaries in a rectangular grid. We put this method into an abstraction refinement framework and improve it by developing an additional refinement step that employs interval constraint propagation to add information to the abstraction without introducing new grid elements. Moreover, the resultingdoi:10.1145/1210268.1210276 fatcat:4gkpnx6hznh4bknm6jby22skpy