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%
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\begin{isabellebody}%
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%
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\begin{isamarkuptext}%
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\noindent
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Define the datatype of binary trees%
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\end{isamarkuptext}%
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\isacommand{datatype}\ {\isacharprime}a\ tree\ {\isacharequal}\ Tip\ {\isacharbar}\ Node\ {\isachardoublequote}{\isacharprime}a\ tree{\isachardoublequote}\ {\isacharprime}a\ {\isachardoublequote}{\isacharprime}a\ tree{\isachardoublequote}%
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\begin{isamarkuptext}%
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\noindent
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and a function \isa{mirror} that mirrors a binary tree
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by swapping subtrees (recursively). Prove%
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\end{isamarkuptext}%
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\isacommand{lemma}\ mirror{\isacharunderscore}mirror{\isacharcolon}\ {\isachardoublequote}mirror{\isacharparenleft}mirror\ t{\isacharparenright}\ {\isacharequal}\ t{\isachardoublequote}%
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\begin{isamarkuptext}%
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\noindent
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Define a function \isa{flatten} that flattens a tree into a list
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by traversing it in infix order. Prove%
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\end{isamarkuptext}%
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\isacommand{lemma}\ {\isachardoublequote}flatten{\isacharparenleft}mirror\ t{\isacharparenright}\ {\isacharequal}\ rev{\isacharparenleft}flatten\ t{\isacharparenright}{\isachardoublequote}\end{isabellebody}%
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "root"
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%%% End:
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