 (TRL1) and (TRL2′) are essential in a branching time structure with a TRL-function. This may be illustrated using a discrete tense-logic like the one mentioned in section 2. We shall assume that there are two functions, \(\next\) and \(back\), from TIME to TIME such that \(\next(t)\) is the moment just after \(t\) on \(\TRL(t)\), and \(back(t)\) is the moment just before \(t\) on \(\TRL(t)\). The similarity to the “tomorrow” \(T(p)\) and “yesterday” \(Y(p)\) of section 2 – and hence, to Prior’s considerations in (Prior 1967) – is worth noting, even though the functions ranged over propositions rather than times. Starting from an arbitrary moment \(t_0\) we may define \(t_n = \next^n(t_0)\) for \(n = 1,2,3,\ldots.\) It follows from (TRL1) and (TRL2′) that \(\TRL(t_0) = \TRL(t_1) = \TRL(t_2) =\TRL(t_3) = \ldots\) and that \(t_n \in \TRL(t_0)\) for any \(n\). In other words, we might have started from the functions \(\next\) and \(\back\) in order to define the function, \(\TRL\). Taking \(t_0\) as now the function \(\next\) would by iterative use constitute the elements of the future part of \(\TRL(t_0)\). Similarly, the past part of \(\TRL(t_0)\), i.e., PAST\((t_0)\) could be established by iterative use of \(back\), given that the branching time structure is backwards linear (as mentioned in section 3). In consequence, it turns out that there is a nice correspondence between a discrete branching time system defined in terms of \(\TRL\) and \(\lt\) on the one hand, and on the other hand the same system defined in terms of the functions, \(\next\) and \(\back\). In this way, a study of the discrete case leads to an interesting illustration of the idea of the thin red line as well as to an emphasis of the importance of (TRL1) and (TRL2′).