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(* Title: ZF/wf.thy
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ID: $Id$
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Author: Tobias Nipkow and Lawrence C Paulson
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Copyright 1992 University of Cambridge
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Well-founded Recursion
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*)
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WF = Trancl + "mono" +
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consts
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wf :: "i=>o"
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wftrec,wfrec :: "[i, i, [i,i]=>i] =>i"
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is_recfun :: "[i, i, [i,i]=>i, i] =>o"
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the_recfun :: "[i, i, [i,i]=>i] =>i"
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rules
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(*r is a well-founded relation*)
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wf_def "wf(r) == ALL Z. Z=0 | (EX x:Z. ALL y. <y,x>:r --> ~ y:Z)"
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is_recfun_def "is_recfun(r,a,H,f) == \
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\ (f = (lam x: r-``{a}. H(x, restrict(f, r-``{x}))))"
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the_recfun_def "the_recfun(r,a,H) == (THE f.is_recfun(r,a,H,f))"
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wftrec_def "wftrec(r,a,H) == H(a, the_recfun(r,a,H))"
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(*public version. Does not require r to be transitive*)
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wfrec_def "wfrec(r,a,H) == wftrec(r^+, a, %x f. H(x, restrict(f,r-``{x})))"
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end
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