 The objects of our first model of positive set theory are sequences \(s_n\) with each \(s_n\) a type \(n\) set and with \(s_{n+1}\) refining \(s_n\) for each \(n\). We say that \(s \in t\) when \(s_{n} \in t_{n+1}\) for all \(n\). It is straightforward to establish that if \(s_{n} \in t_{n+1}\) or \(s_{n} = t_{n}\) is false, then \(s_k \in t_{k+1}\) or (respectively) \(s_k = t_k\) is false for all \(k \gt n\). More generally, if \(s_m \sim t_n\) is false, then \(s_{m+k} \sim t_{n+k}\) is false for all \(k \ge 0\).