src/HOL/Relation.thy
changeset 1983 f3f7bf0079fa
parent 1695 0f9b9eda2a2c
child 3439 54785105178c
     1.1 --- a/src/HOL/Relation.thy	Thu Sep 12 10:35:11 1996 +0200
     1.2 +++ b/src/HOL/Relation.thy	Thu Sep 12 10:36:06 1996 +0200
     1.3 @@ -1,9 +1,7 @@
     1.4  (*  Title:      Relation.thy
     1.5      ID:         $Id$
     1.6 -    Author:     Riccardo Mattolini, Dip. Sistemi e Informatica
     1.7 -        and     Lawrence C Paulson, Cambridge University Computer Laboratory
     1.8 -    Copyright   1994 Universita' di Firenze
     1.9 -    Copyright   1993  University of Cambridge
    1.10 +    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    1.11 +    Copyright   1996  University of Cambridge
    1.12  *)
    1.13  
    1.14  Relation = Prod +
    1.15 @@ -16,11 +14,11 @@
    1.16      Domain      :: "('a*'b) set => 'a set"
    1.17      Range       :: "('a*'b) set => 'b set"
    1.18  defs
    1.19 -    id_def      "id == {p. ? x. p = (x,x)}"
    1.20 -    comp_def    "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
    1.21 +    id_def        "id == {p. ? x. p = (x,x)}"
    1.22 +    comp_def      "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
    1.23      trans_def     "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
    1.24      converse_def  "converse(r) == {(y,x). (x,y):r}"
    1.25      Domain_def    "Domain(r) == {x. ? y. (x,y):r}"
    1.26      Range_def     "Range(r) == Domain(converse(r))"
    1.27 -    Image_def     "r ^^ s == {y. y:Range(r) &  (? x:s. (x,y):r)}"
    1.28 +    Image_def     "r ^^ s == {y. ? x:s. (x,y):r}"
    1.29  end