\begin{frame}[fragile] \frametitle{Examples} \begin{exampleblock}{$\myall{x}{(A(x) \wedge B(x))} \;\vdash\; \myall{x}{B(x)}$} \mpause[1]{ \begin{tikzpicture} \naturaldeduction{ \proofstep{$\myall{x}{(A(x) \wedge B(x))}$}{premise}; \namedproofbox{$x_0$}{ \proofstep{$A(x_0) \wedge B(x_0)$}{$\forall e\;$ 1}; \proofstep{$B(x_0)$}{$\wedge e\;$ 2}; } \proofstep{$\myall{x}{B(x)}$}{$\forall i\;$ 1--3}; } \end{tikzpicture} } \end{exampleblock} \begin{exampleblock}{} {\small% \begin{verbatim}Theorem ex1 : all x, (A(x) /\ B(x)) -> all x, B(x). \end{verbatim} \pause\pause\vspace{-4ex} \begin{verbatim}Proof. imp_i H. all_i x0. insert HAB (A(x0) /\ B(x0)). f_all_e H. f_con_e2 HAB. Qed.\end{verbatim}% } \end{exampleblock} \end{frame}