I am preparing for an exam where I have a Beta reduction question. The question goes as follows:
$M=(\lambda xy.x(\lambda z.xyz))(\lambda x .xz )(\lambda y.ya)$
I have been working this out and following a solution from my professor. If you notice in the photo below, I am at a point like this:
$\xrightarrow{}_\beta yz[y\leftarrow (\lambda z^\prime.(\lambda y.yz)(\lambda z.z)z^\prime)]$
From here, I assume I substitute all of $y$ with the right hand side
$\xrightarrow{}_\text{sub} (\lambda z^\prime.(\lambda y.yz)(\lambda z.z)z^\prime)z$
Notice the final $z$ initially from $yz$. In my professor's solution, she drops that final $z$. Is this a mistake? Or is it correct to drop that z?
