\begin{frame}
  \frametitle{All, Any, Some}

  This query is equivalent to the previous query (but uses \sql{any}):
  \begin{code}{\textwidth}{}
    \small
    \BUseVerbatim{query2}
  \end{code}  
  \pause
  
  \begin{goal}{}
    Note: $\{\, \sql{all}, \sql{any}, \sql{some}  \,\}$ do \emph{not} extend SQL's expressiveness.\\[1ex]
    The statement
    \begin{tcenter}
      \sql{\underline{$A$ < any} (select \underline{$B$} from $\ldots$ where $\ldots$)}
    \end{tcenter}
    is equivalent to 
    \begin{tcenter}
      \sql{\underline{exists} (select $B$ from $\ldots$ where $\ldots$ \underline{and $A$ < $B$})}
    \end{tcenter}
  \end{goal}
  \pause

  \begin{goal}{}
    The statement \quad \sql{$x$ in $S$} \quad is equivalent to \quad \sql{$x$ = any $S$}.
  \end{goal}
\end{frame}