Multi-viewpoint approaches allow stakeholders to design a system from stakeholder-specific viewpoints. By this, a separation of concerns is achieved, which makes designs more manageable. However, to construct a consistent multi-viewpoint design, the relations between viewpoints must be defined precisely, so that the consistency of designs from these viewpoints can be verified. The goal of this paper is to make the consistency rules between (a slightly adapted version of) the RM-ODP enterprise and computational viewpoints more precise and to make checking the consistency between these viewpoints practically applicable. To achieve this goal, we apply a generic framework for relating viewpoints that includes reusable consistency rules. We implemented the consistency rules in a tool to show their applicability.