\begin{sequent}
\begin{align*}
  \alpha:\Mor~|~ &() \\
  \vdash &\IsIsomorphism\big( \KernelLift( \\
  &\CokernelProjection( \alpha ), \CokernelColift( \KernelEmbedding( \alpha ), \alpha ))\big)
\end{align*}
\end{sequent}

\begin{sequent}
\begin{align*}
  \alpha:\Mor~|~ &() \\
  \vdash &\IsIsomorphism\big( \CokernelColift( \\
  &\KernelEmbedding( \alpha ), \KernelLift( \CokernelProjection( \alpha ), \alpha ))\big)
\end{align*}
\end{sequent}