src/HOL/Relation.thy
 author clasohm Mon, 05 Feb 1996 21:27:16 +0100 changeset 1475 7f5a4cd08209 parent 1454 d0266c81a85e child 1695 0f9b9eda2a2c permissions -rw-r--r--
expanded tabs; renamed subtype to typedef; incorporated Konrad's changes
```
(*  Title:      Relation.thy
ID:         \$Id\$
Author:     Riccardo Mattolini, Dip. Sistemi e Informatica
and     Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright   1994 Universita' di Firenze
Copyright   1993  University of Cambridge
*)

Relation = Prod +
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*)
converse    :: "('a * 'b)set => ('b * 'a)set"
"^^"        :: "[('a * 'b) set, 'a set] => 'b set" (infixl 90)
Domain      :: "('a * 'b) set => 'a set"
Range       :: "('a * 'b) set => 'b set"
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)"
converse_def  "converse(r) == {(y,x). (x,y):r}"
Domain_def    "Domain(r) == {x. ? y. (x,y):r}"
Range_def     "Range(r) == Domain(converse(r))"
Image_def     "r ^^ s == {y. y:Range(r) &  (? x:s. (x,y):r)}"
end
```