|
0
|
1 |
(* Title: ZF/trancl.thy
|
|
|
2 |
ID: $Id$
|
|
|
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
|
|
|
4 |
Copyright 1992 University of Cambridge
|
|
|
5 |
|
|
|
6 |
Transitive closure of a relation
|
|
|
7 |
*)
|
|
|
8 |
|
|
435
|
9 |
Trancl = Fixedpt + Perm + "mono" + Rel +
|
|
0
|
10 |
consts
|
|
435
|
11 |
rtrancl :: "i=>i" ("(_^*)" [100] 100) (*refl/transitive closure*)
|
|
|
12 |
trancl :: "i=>i" ("(_^+)" [100] 100) (*transitive closure*)
|
|
0
|
13 |
|
|
753
|
14 |
defs
|
|
0
|
15 |
rtrancl_def "r^* == lfp(field(r)*field(r), %s. id(field(r)) Un (r O s))"
|
|
|
16 |
trancl_def "r^+ == r O r^*"
|
|
|
17 |
end
|