--- a/src/HOL/Relation.thy Thu Jan 08 17:47:22 1998 +0100
+++ b/src/HOL/Relation.thy Thu Jan 08 17:56:32 1998 +0100
@@ -8,17 +8,19 @@
consts
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*)
inverse :: "('a*'b) set => ('b*'a) set" ("(_^-1)" [1000] 999)
"^^" :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
Domain :: "('a*'b) set => 'a set"
Range :: "('a*'b) set => 'b set"
+ trans :: "('a * 'a)set => bool" (*transitivity predicate*)
+ Univalent :: "('a * 'b)set => bool"
defs
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)"
inverse_def "r^-1 == {(y,x). (x,y):r}"
Domain_def "Domain(r) == {x. ? y. (x,y):r}"
Range_def "Range(r) == Domain(r^-1)"
Image_def "r ^^ s == {y. ? x:s. (x,y):r}"
+ trans_def "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
+ Univalent_def "Univalent r == !x y. (x,y):r --> (!z. (x,z):r --> y=z)"
end