In the book Probabilistic Graphical Models from Koller and Friedmann they state on page 117:
When characterizing the independencies in a Bayesian network, we provided two definitions: the local independencies (watch node is independent of its nodescendants given its parents), and the global indendencies induced by d-separation. As we showed, these two sets of independencies are equivalent, in that one implies the other
While I understand the direction local => global, but I cannot see how can prove global => local. Can anybody give me a hint?