src/ZF/WF.thy
 changeset 0 a5a9c433f639 child 124 858ab9a9b047
```     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/ZF/WF.thy	Thu Sep 16 12:20:38 1993 +0200
1.3 @@ -0,0 +1,30 @@
1.4 +(*  Title: 	ZF/wf.thy
1.5 +    ID:         \$Id\$
1.6 +    Author: 	Tobias Nipkow and Lawrence C Paulson
1.7 +    Copyright   1992  University of Cambridge
1.8 +
1.9 +Well-founded Recursion
1.10 +*)
1.11 +
1.12 +WF = Trancl +
1.13 +consts
1.14 +    wf		 ::      "i=>o"
1.15 +    wftrec,wfrec ::      "[i, i, [i,i]=>i] =>i"
1.16 +    is_recfun    ::      "[i, i, [i,i]=>i, i] =>o"
1.17 +    the_recfun   ::      "[i, i, [i,i]=>i] =>i"
1.18 +
1.19 +rules
1.20 +  (*r is a well-founded relation*)
1.21 +  wf_def	 "wf(r) == ALL Z. Z=0 | (EX x:Z. ALL y. <y,x>:r --> ~ y:Z)"
1.22 +
1.23 +  is_recfun_def  "is_recfun(r,a,H,f) == \
1.24 +\   			(f = (lam x: r-``{a}. H(x, restrict(f, r-``{x}))))"
1.25 +
1.26 +  the_recfun_def "the_recfun(r,a,H) == (THE f.is_recfun(r,a,H,f))"
1.27 +
1.28 +  wftrec_def  	 "wftrec(r,a,H) == H(a, the_recfun(r,a,H))"
1.29 +
1.30 +  (*public version.  Does not require r to be transitive*)
1.31 +  wfrec_def "wfrec(r,a,H) == wftrec(r^+, a, %x f. H(x, restrict(f,r-``{x})))"
1.32 +
1.33 +end
```