--- 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