src/ZF/WF.thy
author clasohm
Thu, 16 Sep 1993 12:20:38 +0200
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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 +
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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