s2[V 1], i.e. s1 ∈ f (s2). Then (cid:3)s1, t1, a(cid:4) ∈ E1, where t1 = s1 (cid:4) post(a). Since  R(a, g(a)) holds by deﬁnition it follows that τ is 
R↓. Then also suppose  R((cid:2), g(a)) holds for some (cid:2). The only possibility is that (cid:2) = a. We already know that (cid:3)s1, t1, a(cid:4) ∈ E1. 
We  get  t1 = s1 (cid:4) post(a) = s2[V 1] (cid:4) (post(a) ∪ postM (a))[V 1] = s2[V 1] (cid:4) post(g(a))[V 1] = (s2 (cid:4) post(g(a)))[V 1] = t2[V 1]. 
Hence, t1 ∈ f (t2). It follows that τ is C↓. (cid:2)
A-framework-for-analysing-state-abstraction-metho_2022_Artificial-Intelligen