Some explanations needed about Negation in Gentzen's Natural Deduction rules
I'm guessing your first rule is:


  \begin{align*}
&amp;[A]\\
&amp;~~\vdots\\
&amp;~\bot\\
&amp;\overline{\lnot A}\qquad (I\lnot)
\end{align*}


This means that in order to derive $\lnot A$ one must first assume $A$ (that is $[A]$) and derive a contradiction ($\bot$), the dots between mean a finite number of steps. 


  $$ \frac{A \quad \lnot A}{D} \qquad (E\lnot) $$


This latter rule with $D$ seems to be ex falso quodlibet, since:

$$ \frac{A \quad \lnot A}{\bot} \qquad (E\lnot) $$

therefore:

$$ \frac{\bot}{D} $$

it says that you can derive anything (some $D$) from a contradiction.

Those $(I\circ)$ and $(E\circ)$, where $\circ$ is some operation mean Introduction-Elimination rules. In Gentzen's formulations all rules come in pairs.