src/HOL/Relation.thy
 changeset 4528 ff22e16c5f2f parent 3499 ce1664057431 child 4746 a5dcd7e4a37d
```     1.1 --- a/src/HOL/Relation.thy	Thu Jan 08 17:47:22 1998 +0100
1.2 +++ b/src/HOL/Relation.thy	Thu Jan 08 17:56:32 1998 +0100
1.3 @@ -8,17 +8,19 @@
1.4  consts
1.5      id          :: "('a * 'a)set"               (*the identity relation*)
1.6      O           :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
1.7 -    trans       :: "('a * 'a)set => bool"       (*transitivity predicate*)
1.8      inverse    :: "('a*'b) set => ('b*'a) set"     ("(_^-1)" [1000] 999)
1.9      "^^"        :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
1.10      Domain      :: "('a*'b) set => 'a set"
1.11      Range       :: "('a*'b) set => 'b set"
1.12 +    trans       :: "('a * 'a)set => bool"       (*transitivity predicate*)
1.13 +    Univalent   :: "('a * 'b)set => bool"
1.14  defs
1.15      id_def        "id == {p. ? x. p = (x,x)}"
1.16      comp_def      "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
1.17 -    trans_def     "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
1.18      inverse_def   "r^-1 == {(y,x). (x,y):r}"
1.19      Domain_def    "Domain(r) == {x. ? y. (x,y):r}"
1.20      Range_def     "Range(r) == Domain(r^-1)"
1.21      Image_def     "r ^^ s == {y. ? x:s. (x,y):r}"
1.22 +    trans_def     "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
1.23 +    Univalent_def "Univalent r == !x y. (x,y):r --> (!z. (x,z):r --> y=z)"
1.24  end
```