Let $R$ be a unital ring. Let $P'$, $P$, and $P''$ be finitely generated projective left $R$-modules, and let $i:P'\to P$ and $p:P\to P''$ be $R$-linear maps such that
paragraph
admin
\begin{align*}
0 \longrightarrow P' \xrightarrow{i} P \xrightarrow{p} P'' \longrightarrow 0
\end{align*}
latex_env
admin
is a short exact sequence of left $R$-modules. Then, in $K_0(R)$,