\begin{frame}
  \frametitle{For All \& Implication}

  \begin{goal}{}
    SQL does also not have $\Rightarrow$. The commonly used pattern
    \begin{salign}
      \forall\,X\,(\alpha \Rightarrow \beta)
    \end{salign}
    becomes
    \begin{salign}
      &\;\;\,\forall\,X\,(\alpha \Rightarrow \beta) \\
      \equiv\;\; &\neg\exists\,X\,\neg(\alpha \Rightarrow \beta) \\
      \equiv\;\; &\neg\exists\,X\,\neg(\neg \alpha \vee \beta) \\
      \equiv\;\; &\neg\exists\,X\,(\alpha \wedge \neg\beta) 
    \end{salign}
  \end{goal}
\end{frame}