src/ZF/wf.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/wf.thy	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,30 @@
+(*  Title: 	ZF/wf.thy
+    ID:         $Id$
+    Author: 	Tobias Nipkow and Lawrence C Paulson
+    Copyright   1992  University of Cambridge
+
+Well-founded Recursion
+*)
+
+WF = Trancl +
+consts
+    wf		 ::      "i=>o"
+    wftrec,wfrec ::      "[i, i, [i,i]=>i] =>i"
+    is_recfun    ::      "[i, i, [i,i]=>i, i] =>o"
+    the_recfun   ::      "[i, i, [i,i]=>i] =>i"
+
+rules
+  (*r is a well-founded relation*)
+  wf_def	 "wf(r) == ALL Z. Z=0 | (EX x:Z. ALL y. <y,x>:r --> ~ y:Z)"
+
+  is_recfun_def  "is_recfun(r,a,H,f) == \
+\   			(f = (lam x: r-``{a}. H(x, restrict(f, r-``{x}))))"
+
+  the_recfun_def "the_recfun(r,a,H) == (THE f.is_recfun(r,a,H,f))"
+
+  wftrec_def  	 "wftrec(r,a,H) == H(a, the_recfun(r,a,H))"
+
+  (*public version.  Does not require r to be transitive*)
+  wfrec_def "wfrec(r,a,H) == wftrec(r^+, a, %x f. H(x, restrict(f,r-``{x})))"
+
+end