It is known that, to prove that two sets are equal, we need to show that they are subset of each other. Here we have, intersection of cartesian products on the left side and cartesian product of intersections of sets on the right side, I know the definitions here that is:

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> Cartesian Product: If $A$ and $B$ are any two sets, then $A\times B=$ {$ (a,b), a \in A, b \in B$ }.
> Intersection of sets: $A \cap B=${$ x\colon x \in A, x \in B $}.
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but don't know how to prove that.