 then such an entity would perforce be an atom. Accordingly, no atomless mereology is compatible with this assumption. But it bears emphasis that (P.10) is at odds with a host of other theories as well. For, given (P.10), the Antisymmetry axiom (P.3) will immediately entail that the atom in question is unique, while the Reflexivity axiom (P.1) will entail that it overlaps everything, hence that everything overlaps everything. This means that under such axioms the Supplementation principle (P.4) cannot be satisfied except in models whose domain includes a single element. Indeed, this is also true of the weaker Quasi-supplementation principle, (P.4d). It follows, therefore, that the result of adding (P.10) to any theory at least as strong as (P.1) + (P.3) + (P.4d), and a fortiori to MM and any extension thereof, will immediately collapse to triviality in view of the following corollary: