But why do you care that the set is empty (in the abstract, obviously if there was a reason you'd expect the set to be non-empty, that's a different thing)? Th

But why do you care that the set is empty (in the abstract, obviously if there was a reason you'd expect the set to be non-empty, that's a different thing)? The trick is to think about invariants and state, which if you frame it that way, the empty set case implies there is only a single state.