\begin{isabelle}%
%
\begin{isamarkuptext}%
\noindent
Define the datatype of binary trees%
\end{isamarkuptext}%
\isacommand{datatype}~'a~tree~=~Tip~|~Node~{"}'a~tree{"}~'a~{"}'a~tree{"}%
\begin{isamarkuptext}%
\noindent
and a function \isa{mirror} that mirrors a binary tree
by swapping subtrees (recursively). Prove%
\end{isamarkuptext}%
\isacommand{lemma}~mirror\_mirror:~{"}mirror(mirror~t)~=~t{"}%
\begin{isamarkuptext}%
\noindent
Define a function \isa{flatten} that flattens a tree into a list
by traversing it in infix order. Prove%
\end{isamarkuptext}%
\isacommand{lemma}~{"}flatten(mirror~t)~=~rev(flatten~t){"}\end{isabelle}%
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