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