In the topic of divisibility. Suppose I starts with $a \mid n$, then I manipulate it into $a \mid m$, then $a \mid s$, and finally $a \mid t$. Should I write my train of thought as
$$ \begin{align} a \mid n &\implies a \mid m \\ &\implies a \mid s \\ &\implies a \mid t. \end{align} $$
Or can I just shorthanded it (in the same manner as equality) into
$$ \begin{align} a &\mid n \\ &\mid m \\ &\mid s \\ &\mid t. \end{align} $$
Can I do that? Should I do that? Anyone done that before?
If it is the case that $a$ divides $n$ and $n$ divides $m$ and $m$ divides $s$ and $s$ divides $t$, then you can write $a\mid n\mid m\mid s\mid t$ and that's perfectly understandable. (Chaining like this really works for transitive binary relations.) But I wouldn't write this vertically as you've done in the second equation.
On the other hand, if you're proving that all of $n$, $m$, $s$, and $t$ are multiples of $a$ without saying that they divide one another, then the first way (with implication signs) seems reasonable.