--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/trancl.thy Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,21 @@
+(* Title: ZF/trancl.thy
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1992 University of Cambridge
+
+Transitive closure of a relation
+*)
+
+Trancl = Fixedpt + Perm +
+consts
+ "rtrancl" :: "i=>i" ("(_^*)" [100] 100) (*refl/transitive closure*)
+ "trancl" :: "i=>i" ("(_^+)" [100] 100) (*transitive closure*)
+ "trans" :: "i=>o" (*transitivity predicate*)
+
+rules
+ trans_def "trans(r) == ALL x y z. <x,y>: r --> <y,z>: r --> <x,z>: r"
+
+ rtrancl_def "r^* == lfp(field(r)*field(r), %s. id(field(r)) Un (r O s))"
+
+ trancl_def "r^+ == r O r^*"
+end