\caption{The GUI after running the Alt-Ergo prover on each goal}
\caption{The GUI after running the Alt-Ergo prover on each goal.}
\label{fig:gui3}
\end{figure}
Goal $G_1$ is now marked with a green ``checked'' icon in the
status column. This means that the goal is proved by the Simplify
prover. On the contrary, the two other goals are not proved, they remain
marked with an orange question mark.
You can immediately attempt to prove the remaining goals using another
prover, \eg Alt-Ergo, by clicking on the corresponding button.
Goal $G_3$ should be proved now, but not $G_2$.
Goals $G_1$ and $G_3$ are now marked with a green ``checked'' icon in the
status column. This means that these goals have been proved by Alt-Ergo.
On the contrary, goal $G_2$ is not proved; it remains
marked with a question mark.
You could attempt to prove $G_2$ using another prover, though it is
obvious here it will not succeed.
\subsection{Applying transformations}
Instead of calling a prover on a goal, you can apply a transformation
to it. Since $G_2$ is a conjunction, a possibility is to split it
into subgoals. You can do that by clicking on the \textsf{Split}
button of section ``Transformations'' of the left toolbar. Now you
have two subgoals, and you can try again a prover on them, for example
Simplify. We already have a lot of goals and proof attempts, so it is a good idea to close the sub-trees which are already proved: this can be done by the menu \textsf{View/Collapse proved goals}, or even better by its shortcut ``Ctrl-C''.
You should see now what is displayed on Figure~\ref{fig:gui4}.
into subgoals. You can do that by selecting \textsf{Split} in the
\texttt{Strategies} sub-menu of the context menu. Now you have two
subgoals, and you can try again a prover on them, for example
Alt-Ergo. We already have a lot of goals and proof attempts, so it is
a good idea to close the sub-trees which are already proved: this can
be done by the menu \textsf{View/Collapse proved goals}, or even
better by its shortcut ``Ctrl-C''. You should see now what is
