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(* Title: ZF/fixedpt.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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Least and greatest fixed points


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*)


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Fixedpt = ZF +


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consts


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bnd_mono :: "[i,i=>i]=>o"


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lfp, gfp :: "[i,i=>i]=>i"


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rules


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(*monotone operator from Pow(D) to itself*)


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bnd_mono_def


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"bnd_mono(D,h) == h(D)<=D & (ALL W X. W<=X > X<=D > h(W) <= h(X))"


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lfp_def "lfp(D,h) == Inter({X: Pow(D). h(X) <= X})"


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gfp_def "gfp(D,h) == Union({X: Pow(D). X <= h(X)})"


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end
