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\begin{isabelle}%
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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}~'a~tree~=~Tip~|~Node~{"}'a~tree{"}~'a~{"}'a~tree{"}%
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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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9493
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\isacommand{lemma}~mirror\_mirror:~{"}mirror(mirror~t)~=~t{"}%
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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}~{"}flatten(mirror~t)~=~rev(flatten~t){"}\end{isabelle}%
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9145
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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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