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(* Title: HOL/Induct/Tree.thy
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ID: $Id$
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Author: Stefan Berghofer, TU Muenchen
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Copyright 1999 TU Muenchen
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Infinitely branching trees
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*)
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Tree = Main +
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datatype 'a tree = Atom 'a | Branch "nat => 'a tree"
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consts
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map_tree :: "('a => 'b) => 'a tree => 'b tree"
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primrec
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"map_tree f (Atom a) = Atom (f a)"
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"map_tree f (Branch ts) = Branch (%x. map_tree f (ts x))"
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consts
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exists_tree :: "('a => bool) => 'a tree => bool"
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primrec
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"exists_tree P (Atom a) = P a"
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"exists_tree P (Branch ts) = (? x. exists_tree P (ts x))"
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end
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