
diff -r f04b33ce250f -r a4dc62a46ee4 Trancl.thy
--- a/Trancl.thy	Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,26 +0,0 @@
-(*  Title: 	HOL/trancl.thy
-    ID:         $Id$
-    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1992  University of Cambridge
-
-Transitive closure of a relation
-
-rtrancl is refl/transitive closure;  trancl is transitive closure
-*)
-
-Trancl = Lfp + Prod + 
-consts
-    trans   :: "('a * 'a)set => bool" 	(*transitivity predicate*)
-    id	    :: "('a * 'a)set"
-    rtrancl :: "('a * 'a)set => ('a * 'a)set"	("(_^*)" [100] 100)
-    trancl  :: "('a * 'a)set => ('a * 'a)set"	("(_^+)" [100] 100)  
-    O	    :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
-defs   
-trans_def	"trans(r) == (!x y z. <x,y>:r --> <y,z>:r --> <x,z>:r)"
-comp_def	(*composition of relations*)
-		"r O s == {xz. ? x y z. xz = <x,z> & <x,y>:s & <y,z>:r}"
-id_def		(*the identity relation*)
-		"id == {p. ? x. p = <x,x>}"
-rtrancl_def	"r^* == lfp(%s. id Un (r O s))"
-trancl_def	"r^+ == r O rtrancl(r)"
-end




