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(* Title: ZF/trancl.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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Transitive closure of a relation
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*)
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Trancl = Fixedpt + Perm + "mono" +
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consts
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"rtrancl" :: "i=>i" ("(_^*)" [100] 100) (*refl/transitive closure*)
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"trancl" :: "i=>i" ("(_^+)" [100] 100) (*transitive closure*)
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"trans" :: "i=>o" (*transitivity predicate*)
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rules
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trans_def "trans(r) == ALL x y z. <x,y>: r --> <y,z>: r --> <x,z>: r"
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rtrancl_def "r^* == lfp(field(r)*field(r), %s. id(field(r)) Un (r O s))"
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trancl_def "r^+ == r O r^*"
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end
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