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(* Title: Relation.thy
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ID: $Id$
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Author: Riccardo Mattolini, Dip. Sistemi e Informatica
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and Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1994 Universita' di Firenze
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Copyright 1993 University of Cambridge
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Functions represented as relations in Higher-Order Set Theory
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*)
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Relation = Trancl +
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consts
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converse :: "('a*'a) set => ('a*'a) set"
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"^^" :: "[('a*'a) set,'a set] => 'a set" (infixl 90)
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Domain :: "('a*'a) set => 'a set"
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Range :: "('a*'a) set => 'a set"
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defs
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converse_def "converse(r) == {z. (? w:r. ? x y. w=<x,y> & z=<y,x>)}"
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Domain_def "Domain(r) == {z. ! x. (z=x --> (? y. <x,y>:r))}"
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Range_def "Range(r) == Domain(converse(r))"
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Image_def "r ^^ s == {y. y:Range(r) & (? x:s. <x,y>:r)}"
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end
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