Proof of Theorem SMEZV

We prove this theorem by breaking up the analysis into two cases. The first seems too trivial, and it is, but the logic of the argument is still legitimate.

Case 1. Suppose $\alpha=0$. In this case our conclusion is true (the first part of the either/or is true) and we are done. That was easy.

Case 2. Suppose $\alpha\neq 0$. \begin{align*} \vect{u} &=1\vect{u} &&\knowl{./knowls/property.O.knowl}{\text{Property O}}\\ &=\left(\frac{1}{\alpha}\alpha\right)\vect{u} &&\alpha\neq 0, <acroref type="property" acro="MICN" />\\ &=\frac{1}{\alpha}\left(\alpha\vect{u}\right) &&\knowl{./knowls/property.SMA.knowl}{\text{Property SMA}}\\ &=\frac{1}{\alpha}\left(\zerovector\right) &&\text{Hypothesis}\\ &=\zerovector&&\knowl{./knowls/theorem.ZVSM.knowl}{\text{Theorem ZVSM}} \end{align*}

So in this case, the conclusion is true (the second part of the either/or is true) and we are done since the conclusion was true in each of the two cases.