 In the introduction we encountered one type of puzzle about identity across time: the case of Cup and Tcup. The puzzle arose because we envisaged Cup losing one of its parts, and coming to have the same material constitution (being, for example, composed of exactly the same atoms as), and spatial boundaries as Tcup. Call this the cup case. Let us say that a and b are coincident at a time t just in case the following holds. Something is a proper part of a at t if and only if it is a proper part of b at that same time. Cup and Tcup are coincident at the later time since something at that later time is, for example, and atomic part of a if and only if it is an atomic part of b.