I am trying to write a proof that $a \vert b$ if and only if $da \vert db$. This is what I have so far:
$da \vert db$ if and only if $\lfloor db / da \rfloor = db / da$
$\frac{db}{da} = \frac{b}{a}$ and therefore $\lfloor b / a \rfloor = b / a$
consequently $a \vert b$
I feel like this addresses the if but not the and only if part of the initial statement. Where do I go from here?