 In MHI property composition and property decomposition hold because the actualization rule only applies to elemental systems: the definite-valued properties of composite systems are selected on the basis of those of the elemental components and following the usual quantum assumption according to which the observable \(A^1\) of a subsystem \(S^1\) and the observable \(A = A^1 \otimes I^2\) of the composite system \(S = S^1 S^2\) represent the same property (Ardenghi and Lombardi 2011).