We have recently developed an object-oriented refinement calculus called rCOS. With rCOS, we formalize the object-orient design principles and patterns as refinement laws. rCOS has been proven to provide formal support to software design and program refactoring. All these features together show that rCOS can be used as a formal framework for the use-cased driven,incremental and iterative Rational Unified Process (RUP). In this paper, we apply rCOS to a step-wised development of a Point of Sale Terminal (POST) system and demonstrate how to apply the refinement laws for design and refactoring, from a requirement model to a design model, and finally, to the implementation in Visual C\#.