Consider the Grothendieck ring $K_0(\mathcal{V}_k)$ of $$-varieties, with $k$ a field. Then for any $$-variety $$, and closed subset $$ of $$, we have the relation \begin{equation} []=[ \setminus ]+[], \end{equation} where $[]$ means the isomorphism class of $$.
This might be a question about terminology in the end, but my question is: when defining $K_0(\mathcal{V}_k)$, one starts from the free abelian group $F_k$ with generators the isomorphism classes of $k$-varieties. Why is $F_k$ closed under all relations of the above type ?