The "calculus" of sums, i.e. $\sum_{j=0}^{2k}-\sum_{j=0}^k$

Question

I have a question regarding the "calculus" of sums. Namely, if

$$x:=\sum_{j=0}^{2k}\alpha_j\qquad\text{and}\qquad y=\sum_{j=0}^k\alpha_j,$$ is it generally correct that $$x-y=\left(\sum_{j=0}^{2k}-\sum_{j=0}^k \right)\alpha_j=\sum_{j=0}^{2k-k}\alpha_j=\sum_{j=0}^k\alpha_j?$$