I would like to write $\{(i, x, y) \mid (i,x) \in \{(1,1), (2,1), (2,2)\}\}$ where $y$ could be any (integer) value. Is there a shorter way to write that...
Also for $\{(i, x, y) \mid i = 2, x = 1\}$, can we write $\{(2, 1, y)\}$ which looks like a singleton?