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

  \vspace{-.5ex}
  \begin{goal}{}
    Lossless split guarantees that the schema after splitting
    can represent all DB states that were possible before.
  \end{goal}
  \begin{itemize}
    \item we can translate states from the old into the new schema
    \item old schema can be ``simulated'' via views
  \end{itemize}
  \bigskip
  \pause
  
  \begin{goal}{}
    Lossless splits can lead to \emph{more general schemas}!
    \begin{itemize}
      \item the new schema allows states which do not correspond to the state in the old schema
    \end{itemize}
  \end{goal}  
  
  \begin{exampleblock}{}
    \recallexamplephone
    \emph{We may now store instructors and phone numbers without any affiliation to courses.}
  \end{exampleblock}

  % \begin{itemize}
  % \item If instructors without courses are possible in the real world,
  %   the decomposition removes a fault in the old schema (insertion and
  %   update anomalies).
  % 
  % \item If they are not,
  %   \begin{itemize}
  %   \item a new constraint is needed that is not necessarily easier to
  %     enforce than the FD, but 
  %   \item at least the redundancy is avoided (update anomaly).
  %   \end{itemize}
  % \end{itemize}
\end{frame}