 In the presence of Commutation, a double implication pair \((\rightarrow , \leftarrow)\) collapses into single implication \(\rightarrow\). In the presence of all of the structural rules, fusion, \(\otimes\), collapses into Boolean conjunction, \(\wedge\). In this case, the residuation conditions outlined in (5) and (6) collapse into a mono-directional function. 