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(* Title: CCL/wfd.thy
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ID: $Id$
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Author: Martin Coen, Cambridge University Computer Laboratory
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Copyright 1993 University of Cambridge
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Well-founded relations in CCL.
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*)
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Wfd = Trancl + Type +
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consts
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(*** Predicates ***)
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Wfd :: "[i set] => o"
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(*** Relations ***)
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wf :: "[i set] => i set"
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wmap :: "[i=>i,i set] => i set"
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"**" :: "[i set,i set] => i set" (infixl 70)
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NatPR :: "i set"
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ListPR :: "i set => i set"
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rules
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Wfd_def
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"Wfd(R) == ALL P.(ALL x.(ALL y.<y,x> : R --> y:P) --> x:P) --> (ALL a.a:P)"
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wf_def "wf(R) == {x.x:R & Wfd(R)}"
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wmap_def "wmap(f,R) == {p. EX x y. p=<x,y> & <f(x),f(y)> : R}"
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lex_def
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"ra**rb == {p. EX a a' b b'.p = <<a,b>,<a',b'>> & (<a,a'> : ra | (a=a' & <b,b'> : rb))}"
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NatPR_def "NatPR == {p.EX x:Nat. p=<x,succ(x)>}"
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ListPR_def "ListPR(A) == {p.EX h:A.EX t:List(A). p=<t,h$t>}"
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end
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