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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 +


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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
