 Where \(z \Vdash A\) and \(w \Vdash D\), this will be the case for all \(x, y, v\) s.t. \(x \Vdash A \rightarrow\), \(y \Vdash B \rightarrow C\), \(v \Vdash C \rightarrow D\). This is just the first step required to demonstrate that channel theory, and its underlying substructural logic, form a category. 