Consider the following conditional independencies of four Random Variables A, B, C, D.
$$A \perp B \mid C, D$$ $$A \perp D \mid B, C$$
Can the following concluded from the given independencies?
$P(A, B, C, D) =P(A, C, D) P(B \mid A, D)$ and $P(B \mid A, C) = P(B \mid C, D)$
I tried to derive the conclusions, but unsuccessful. But can I gaurentee that I can never get the conclusions?