And say that, in, and say that H is an I-map or independency map of P if P satisfies all of the independencies that we can read off the graph structure of H. And the theorem that we just proved, restated, says that if P factorizes over H then H is an I-map for P because we have shown that if, P factorizes over H then it satisfies all of the independencies that one can read off the graph H. Now in the context of 