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(* Title : Zorn.thy
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7219
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ID : $Id$
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5979
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Author : Jacques D. Fleuriot
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Copyright : 1998 University of Cambridge
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Description : Zorn's Lemma -- See lcp's Zorn.thy in ZF
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*)
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7564
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Zorn = Main +
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5979
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constdefs
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chain :: 'a set => 'a set set
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"chain S == {F. F <= S & (ALL x: F. ALL y: F. x <= y | y <= x)}"
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super :: ['a set,'a set] => (('a set) set)
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"super S c == {d. d: chain(S) & c < d}"
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maxchain :: 'a set => 'a set set
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"maxchain S == {c. c: chain S & super S c = {}}"
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succ :: ['a set,'a set] => 'a set
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"succ S c == if (c ~: chain S| c: maxchain S)
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then c else (@c'. c': (super S c))"
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consts
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"TFin" :: 'a set => 'a set set
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inductive "TFin(S)"
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intrs
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succI "x : TFin S ==> succ S x : TFin S"
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Pow_UnionI "Y : Pow(TFin S) ==> Union(Y) : TFin S"
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monos Pow_mono
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end
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