In addition to the ever increasing software complexity, there has been a significant increase in the demand for more flexible and dependable software systems. Therefore, it is necessary to be able not only to achieve high quality but also to rigorously demonstrate that high quality has been achieved. While relatively mature techniques exist for certifying hardware systems, methods of certifying software systems are still being actively researched. More importantly, even though substantial research has been carried out to reduce the complexity of the software system through decomposition, one major hurdle is the need to certify the overall system on the basis of the component properties. Our early research introduced a novel approach that enhances the "accessibility" of each component, so that the properties of a system can be mathematically inferred from those of its components. In this paper, we show the validity of these mathematical inference expressions through different classes of components and system using Java?s exception handling, an implementation of pipes-and-filters architecture, and a simple sorting selector.