--- a/src/HOL/Relation.thy Thu Sep 12 10:35:11 1996 +0200
+++ b/src/HOL/Relation.thy Thu Sep 12 10:36:06 1996 +0200
@@ -1,9 +1,7 @@
(* 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
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1996 University of Cambridge
*)
Relation = Prod +
@@ -16,11 +14,11 @@
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}"
+ 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)}"
+ Image_def "r ^^ s == {y. ? x:s. (x,y):r}"
end