Note that it only applies this if a graph node only has a single outgoing edge that is a match, and doesn’t provide a proof specific for the case of graphs. This is unclear: ‘whether a successor state is a match’ can mean ‘whether there exists a successor state that is a match’ or ‘whether a given successor state is a match’. Since Dijkstra computes states in order of \(d\), if we prioritize states closer to the end, it is sufficient to simply check if all of the \(T_x\) are computed.