\begin{frame}
  \frametitle{Splitting Relations: Lossless Splits}

  \begin{exampleblock}{Lossless split condition satisfied}
    \recallexamplephone
    \medskip
    \pause
    
    The lossless split condition is satisfied since
    \begin{tcenter}
      $\{ \sql{courseNr}, \sql{title}, \sql{instructor} \} \;\cap\; \{ \sql{instructor}, \sql{phone} \}$ \\
      $= \{ \sql{instructor} \} $
    \end{tcenter}
    and $\sql{instructor}$ is a key of the table \sql{Instructors}.
  \end{exampleblock}
  \pause
  
  \begin{goal}{}
    All splits initiated by the \emph{table decomposition method} 
    % for transforming relations into BCNF 
    satisfy the condition of the decomposition theorem.
  \end{goal}

  It is \emph{always possible} to transform a relation into BCNF
  by lossless splitting.
\end{frame}