As I will write constraint sets very often, I would like to make sure that I respect the convention.
First, I would like to represent a set of constraints and their relation are conjunction. For instance, $[1 \leq i \leq 2, 1 \leq j \leq 2]$ means the set of all possible pairs of $(i,j)$: $\{(1,1); (1,2); (2,1); (2,2)\}$.
Do you think $[1 \leq i \leq 2, 1 \leq j \leq 2]$ or $\{1 \leq i \leq 2; 1 \leq j \leq 2\}$ is better?
Let's denote the above constraint set (a). Second, I want to say another constraint set "forall i, j satisfying (a), $x \leq i$ and $x \leq j$", which is actually $(-\infty, 1]$ for $x$.
Do you think $\forall i, j \in (a), [x \leq i, x \leq j]$ is the best way to formalize that?