38/158
\begin{frame}
   \frametitle{Truth of Diamonds: $\some \phi$}

  \begin{goal}{$w \fc \some \phi$}
    The formula \;\;$\some \phi$ is true in world $w$\;\;
    if there exists a world $w'$\;\; such that \;\;$R(w,w')$ \;\;and\;\; $\phi$ is true in $w'$.
  \end{goal}
  \pause
  
  \begin{block}{}
  As a formula:\quad
    $w \fc \some \phi \quad\DARKRED{\iff}\quad
    \myex{w'}{\big( R(w,w') \;\wedge\; w' \fc \phi \big)}$
  \end{block}
  \pause
  
  \begin{exampleblock}{}
    \exampleA
    
    For example,
    \begin{talign}
      \mpause[1]{ w_1  &\mpause{\fc}  \some\lab{p} } &
      \mpause{ w_3  &\mpause{\notfc} \some\lab{p} } &
      \mpause{ w_1  &\mpause{\fc}     \some\lab{q} } &
      \mpause{ w_3  &\mpause{\fc}     \some\lab{q} }
    \end{talign}
  \end{exampleblock}
\end{frame}