I have a bayesian belief network with 4 binary variables $A, B, C, D$. I now need to proof that for joint probability distributions factorized according the Bayesian network given below the conditional independency $A⊥⊥D|C$ always holds.
This by using factorization. Now I know that
$$p(A,B,C,D) = p(A)p(B)p(C|A,B)p(D|C)$$
but how can I go from that to proving that $p(A,D|C) = p(A|C)p(D|C)$ (definition conditional independence)