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(*  Title:      ZF/ex/BT.thy
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1992  University of Cambridge
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Binary trees
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*)
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6112
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BT = Main +
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consts
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    bt          :: i=>i
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datatype
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  "bt(A)" = Lf  |  Br ("a: A",  "t1: bt(A)",  "t2: bt(A)")
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consts
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    n_nodes     :: i=>i
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    n_leaves    :: i=>i
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    bt_reflect  :: i=>i
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primrec
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  "n_nodes(Lf) = 0"
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  "n_nodes(Br(a,l,r)) = succ(n_nodes(l) #+ n_nodes(r))"
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primrec
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  "n_leaves(Lf) = 1"
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  "n_leaves(Br(a,l,r)) = n_leaves(l) #+ n_leaves(r)"
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primrec
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  "bt_reflect(Lf) = Lf"
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  "bt_reflect(Br(a,l,r)) = Br(a, bt_reflect(r), bt_reflect(l))"
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end
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