Solution VS.T23 Robert Beezer

\begin{align*} \zerovector &=\alpha\vect{u} + -\left(\alpha\vect{u}\right)&&\knowl{./knowls/property.AI.knowl}{\text{Property AI}}\\ &=\beta\vect{u} + -\left(\alpha\vect{u}\right)&&\text{Hypothesis}\\ &=\beta\vect{u} + (-1)\left(\alpha\vect{u}\right)&&\knowl{./knowls/theorem.AISM.knowl}{\text{Theorem AISM}}\\ &=\beta\vect{u} + \left((-1)\alpha\right)\vect{u}&&\knowl{./knowls/property.SMA.knowl}{\text{Property SMA}}\\ &=\beta\vect{u} + \left(-\alpha\right)\vect{u}\\ &=\left(\beta-\alpha\right)\vect{u}&&\knowl{./knowls/property.DSA.knowl}{\text{Property DSA}}\\ \end{align*} By hypothesis, $\vect{u}\neq\zerovector$, so Theorem SMEZV implies \begin{align*} 0&=\beta-\alpha\\ \alpha&=\beta \end{align*}