A basic result on divisibility
Recall the definition of divisibility:
For two integers $a$ and $b$
we say $a$ divides $b$ (or $b$ is divisible by $a$)
if and only if $a \neq 0$ and $\exists x[a*x = b]$.
We will use the notation "$a|b$" to express that $a$ divides $b$.
(Sorry for using the same symbol as we sometimes to mean
"or".)
Note that "divides" is a predicate, so $a|b$ gives a
true/false value, like $a = b$ or $a \lt b$.
Go to the whiteboard as a group of 2-3 students and give two
proofs, a prose proof and a full first-order logic proof, of the
following theorem:
For any integers $u$, $v$ and $w$,
if $u|v$ then $u|(v*w)$.