Givan $A$ an array of lists of different length but with the condition that the elements of every list are the same (meaning that if a list in a position $A[i]$ has length $k$ and a list in a position $A[j]$ has length $l$, with $k < l$, the $k$ elements of $A[i]$ are the same as the first $k$ elements of $A[j]$).
How could a I write in a set-theory notation the existence of the longest sublist $p$ in common among every element of the array?