src/ZF/WF.thy
changeset 435 ca5356bd315a
parent 124 858ab9a9b047
child 930 63f02d32509e
--- a/src/ZF/WF.thy	Tue Jun 21 16:26:34 1994 +0200
+++ b/src/ZF/WF.thy	Tue Jun 21 17:20:34 1994 +0200
@@ -1,22 +1,28 @@
 (*  Title: 	ZF/wf.thy
     ID:         $Id$
     Author: 	Tobias Nipkow and Lawrence C Paulson
-    Copyright   1992  University of Cambridge
+    Copyright   1994  University of Cambridge
 
 Well-founded Recursion
 *)
 
-WF = Trancl + "mono" +
+WF = Trancl + "mono" + "equalities" +
 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"
+  wf           :: "i=>o"
+  wf_on        :: "[i,i]=>o"			("wf[_]'(_')")
+
+  wftrec,wfrec :: "[i, i, [i,i]=>i] =>i"
+  wfrec_on     :: "[i, i, i, [i,i]=>i] =>i"	("wfrec[_]'(_,_,_')")
+  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)"
 
+  (*r is well-founded relation over A*)
+  wf_on_def      "wf_on(A,r) == wf(r Int A*A)"
+
   is_recfun_def  "is_recfun(r,a,H,f) == \
 \   			(f = (lam x: r-``{a}. H(x, restrict(f, r-``{x}))))"
 
@@ -27,4 +33,6 @@
   (*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})))"
 
+  wfrec_on_def   "wfrec[A](r,a,H) == wfrec(r Int A*A, a, H)"
+
 end