Proof of Theorem LTTZZ

The two zero vectors in the conclusion of the theorem are different. The first is from $U$ while the second is from $V$. We will subscript the zero vectors in this proof to highlight the distinction. Think about your objects. (This proof is contributed by Mark Shoemaker). \begin{align*} \lt{T}{\zerovector_U} &=\lt{T}{0\zerovector_U} &&\knowl{./knowls/theorem.ZSSM.knowl}{\text{Theorem ZSSM}}\text{ in }U\\ &=0\lt{T}{\zerovector_U} &&\knowl{./knowls/definition.LT.knowl}{\text{Definition LT}}\\ &=\zerovector_V &&\knowl{./knowls/theorem.ZSSM.knowl}{\text{Theorem ZSSM}}\text{ in }V \end{align*}