--- a/src/CCL/Trancl.thy Mon Feb 05 13:44:28 1996 +0100
+++ b/src/CCL/Trancl.thy Mon Feb 05 14:44:09 1996 +0100
@@ -1,6 +1,6 @@
-(* Title: CCL/trancl.thy
+(* Title: CCL/trancl.thy
ID: $Id$
- Author: Martin Coen, Cambridge University Computer Laboratory
+ Author: Martin Coen, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Transitive closure of a relation
@@ -9,20 +9,20 @@
Trancl = CCL +
consts
- trans :: "i set => o" (*transitivity predicate*)
- id :: "i set"
- rtrancl :: "i set => i set" ("(_^*)" [100] 100)
- trancl :: "i set => i set" ("(_^+)" [100] 100)
- O :: "[i set,i set] => i set" (infixr 60)
+ trans :: "i set => o" (*transitivity predicate*)
+ id :: "i set"
+ rtrancl :: "i set => i set" ("(_^*)" [100] 100)
+ trancl :: "i set => i set" ("(_^+)" [100] 100)
+ O :: "[i set,i set] => i set" (infixr 60)
rules
-trans_def "trans(r) == (ALL x y z. <x,y>:r --> <y,z>:r --> <x,z>:r)"
-comp_def (*composition of relations*)
- "r O s == {xz. EX x y z. xz = <x,z> & <x,y>:s & <y,z>:r}"
-id_def (*the identity relation*)
- "id == {p. EX x. p = <x,x>}"
-rtrancl_def "r^* == lfp(%s. id Un (r O s))"
-trancl_def "r^+ == r O rtrancl(r)"
+trans_def "trans(r) == (ALL x y z. <x,y>:r --> <y,z>:r --> <x,z>:r)"
+comp_def (*composition of relations*)
+ "r O s == {xz. EX x y z. xz = <x,z> & <x,y>:s & <y,z>:r}"
+id_def (*the identity relation*)
+ "id == {p. EX x. p = <x,x>}"
+rtrancl_def "r^* == lfp(%s. id Un (r O s))"
+trancl_def "r^+ == r O rtrancl(r)"
end