--- a/src/HOL/Relation.thy Mon Jun 16 14:25:33 1997 +0200
+++ b/src/HOL/Relation.thy Tue Jun 17 09:01:56 1997 +0200
@@ -9,7 +9,7 @@
id :: "('a * 'a)set" (*the identity relation*)
O :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
trans :: "('a * 'a)set => bool" (*transitivity predicate*)
- converse :: "('a*'b) set => ('b*'a) set"
+ inverse :: "('a*'b) set => ('b*'a) set" ("(_^-1)" [1000] 1000)
"^^" :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
Domain :: "('a*'b) set => 'a set"
Range :: "('a*'b) set => 'b set"
@@ -17,8 +17,8 @@
id_def "id == {p. ? x. p = (x,x)}"
comp_def "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
trans_def "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
- converse_def "converse(r) == {(y,x). (x,y):r}"
+ inverse_def "r^-1 == {(y,x). (x,y):r}"
Domain_def "Domain(r) == {x. ? y. (x,y):r}"
- Range_def "Range(r) == Domain(converse(r))"
+ Range_def "Range(r) == Domain(r^-1)"
Image_def "r ^^ s == {y. ? x:s. (x,y):r}"
end