 For i=3, the extension of EM obtained by adding every instance of this schema has a distinguished pedigree and is known in the literature as General Extensional Mereology, or GEM. It corresponds to the classical systems of Leśniewski and of Leonard and Goodman, modulo the underlying logic and choice of primitives. The same theory can be obtained by extending EM with (P.152) instead, for in the presence of extensionality the two schemas are equivalent. Indeed, it turns out that the latter axiomatization is somewhat redundant: given just Transitivity and Supplementation, Unrestricted Sum2 entails all the other axioms, i.e., GEM is the same theory as (P.2) + (P.4) + (P.152). By contrast, extending EM with (P.151) would result in a weaker theory (Figure 8), though one can still get the full strength of GEM with the help of additional axioms. For example, Hovda (2009) shows that the following will do: 