--- a/src/ZF/Trancl.thy Tue Jun 21 16:26:34 1994 +0200
+++ b/src/ZF/Trancl.thy Tue Jun 21 17:20:34 1994 +0200
@@ -6,16 +6,12 @@
Transitive closure of a relation
*)
-Trancl = Fixedpt + Perm + "mono" +
+Trancl = Fixedpt + Perm + "mono" + Rel +
consts
- "rtrancl" :: "i=>i" ("(_^*)" [100] 100) (*refl/transitive closure*)
- "trancl" :: "i=>i" ("(_^+)" [100] 100) (*transitive closure*)
- "trans" :: "i=>o" (*transitivity predicate*)
+ rtrancl :: "i=>i" ("(_^*)" [100] 100) (*refl/transitive closure*)
+ trancl :: "i=>i" ("(_^+)" [100] 100) (*transitive closure*)
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