where does this prove come from: for any kind of value $s,t,u: s/t \land s/u \Rightarrow s/(t+u)$

Question

Can someone explain me why does this arithmetic theory comes from : $s,t,u: s/t \land s/u \Rightarrow s/(t+u)$ in wich s,t,u can have any kind of value.

Answer 1

You can write $$s|t$$ then $$t=ms$$ and $$s|u$$ then $$u=ns$$ and we get $$t+u=s(m+n)=sp'$$ where $m,n,p'$ are integers.