src/ZF/trancl.thy
author clasohm
Thu Sep 16 12:20:38 1993 +0200 (1993-09-16)
changeset 0 a5a9c433f639
child 124 858ab9a9b047
permissions -rw-r--r--
Initial revision
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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