I know how to handle the 2d case: http://www.proofwiki.org/wiki/Set_Difference_of_Cartesian_Products
But I am having trouble simplifying the following:
Let $X=\prod_{1}^\infty X_i, A_i \subset X_i$
How can I simplify/rewrite $X - (A_1 \times A_2 \times \cdots A_n \times X_{n+1} \times X_{n+2} \cdots)$ with unions/intersections?