Prove that the long exact sequence in the statement of the snake lemma is exact at the term $\displaystyle \text{coker}\hspace{.03in}f$. The long exact sequence is: $\displaystyle \text{ker}\hspace{.03in}f \xrightarrow{\alpha_0} \text{ker}\hspace{.03in} g \xrightarrow{\beta_0} \text{ker}\hspace{.03in} h \xrightarrow{\delta} \text{coker}\hspace{.03in} f \xrightarrow{\overline{\alpha'}} \text{coker} \hspace{.03in}g \xrightarrow{\overline{\beta'}} \text{coker}\hspace{.03in} h$. The diagram is below.