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(*<*)
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theory Tree = Main:
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(*>*)
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text{*\noindent
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Define the datatype of binary trees
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*}
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datatype 'a tree = Tip | Node "'a tree" 'a "'a tree";(*<*)
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consts mirror :: "'a tree \\<Rightarrow> 'a tree";
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primrec
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"mirror Tip = Tip"
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"mirror (Node l x r) = Node (mirror l) x (mirror r)";(*>*)
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text{*\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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*}
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lemma mirror_mirror: "mirror(mirror t) = t";
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(*<*)
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apply(induct_tac t);
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apply(auto).;
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end
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(*>*)
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