This particular argument is not talking about farsightedness—when we talk about having more options, each option is talking about the entire journey and exact timesteps, rather than just the destination. Since all the “journeys” starting with the S --> Z action go to Z first, and all the “journeys” starting with the S --> A action go to A first, the isomorphism has to map A to Z and vice versa, so that ϕ(T(S,a1))=T(S,a2).
(What assumption does this correspond to in the theorem? In the theorem, the involution has to map Fa to a subset of Fa′; every possibility in Fa1 starts with A, and every possibility in Fa2 starts with Z, so you need to map A to Z.)
This particular argument is not talking about farsightedness—when we talk about having more options, each option is talking about the entire journey and exact timesteps, rather than just the destination. Since all the “journeys” starting with the S --> Z action go to Z first, and all the “journeys” starting with the S --> A action go to A first, the isomorphism has to map A to Z and vice versa, so that ϕ(T(S,a1))=T(S,a2).
(What assumption does this correspond to in the theorem? In the theorem, the involution has to map Fa to a subset of Fa′; every possibility in Fa1 starts with A, and every possibility in Fa2 starts with Z, so you need to map A to Z.)