A erroneous Suslin scheme

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Surely the question has an easy answer I'm not able to find, but anyway... $R$ is the real line and $N$ the set of natural numbers, $I=N^N$. Let $X\subset R$ be indexed by $I$. For every $a \in I$ be $y_a$ the corresponding point in $X$. The question is: Why $\cup_{a\in I} \cap_{n\in N} \{y_a\}$ is not a Suslin scheme?