More concise way of saying this?

Question

I have written this:

For the one highlighted in red, is there a more compact way of writing it?

Answer 1

In my opinion, I don't think you need that. You can directly define $D$ as

$$ D = \left\{D_i\right\}_{i = 1}^6$$ and you say $D_i = \{x \in \mathbb{Z} | 0 \leq x \leq 9\}$, then there is no need for $\forall i \in \left\{1, 2, \ldots, 6\right\}$.