src/ZF/wf.thy
author clasohm
Thu Sep 16 12:20:38 1993 +0200 (1993-09-16)
changeset 0 a5a9c433f639
child 124 858ab9a9b047
permissions -rw-r--r--
Initial revision
     1 (*  Title: 	ZF/wf.thy
     2     ID:         $Id$
     3     Author: 	Tobias Nipkow and Lawrence C Paulson
     4     Copyright   1992  University of Cambridge
     5 
     6 Well-founded Recursion
     7 *)
     8 
     9 WF = Trancl +
    10 consts
    11     wf		 ::      "i=>o"
    12     wftrec,wfrec ::      "[i, i, [i,i]=>i] =>i"
    13     is_recfun    ::      "[i, i, [i,i]=>i, i] =>o"
    14     the_recfun   ::      "[i, i, [i,i]=>i] =>i"
    15 
    16 rules
    17   (*r is a well-founded relation*)
    18   wf_def	 "wf(r) == ALL Z. Z=0 | (EX x:Z. ALL y. <y,x>:r --> ~ y:Z)"
    19 
    20   is_recfun_def  "is_recfun(r,a,H,f) == \
    21 \   			(f = (lam x: r-``{a}. H(x, restrict(f, r-``{x}))))"
    22 
    23   the_recfun_def "the_recfun(r,a,H) == (THE f.is_recfun(r,a,H,f))"
    24 
    25   wftrec_def  	 "wftrec(r,a,H) == H(a, the_recfun(r,a,H))"
    26 
    27   (*public version.  Does not require r to be transitive*)
    28   wfrec_def "wfrec(r,a,H) == wftrec(r^+, a, %x f. H(x, restrict(f,r-``{x})))"
    29 
    30 end