src/HOL/Relation.thy
changeset 1475 7f5a4cd08209
parent 1454 d0266c81a85e
child 1695 0f9b9eda2a2c
     1.1 --- a/src/HOL/Relation.thy	Mon Feb 05 14:44:09 1996 +0100
     1.2 +++ b/src/HOL/Relation.thy	Mon Feb 05 21:27:16 1996 +0100
     1.3 @@ -1,24 +1,24 @@
     1.4 -(*  Title: 	Relation.thy
     1.5 +(*  Title:      Relation.thy
     1.6      ID:         $Id$
     1.7 -    Author: 	Riccardo Mattolini, Dip. Sistemi e Informatica
     1.8 -        and	Lawrence C Paulson, Cambridge University Computer Laboratory
     1.9 +    Author:     Riccardo Mattolini, Dip. Sistemi e Informatica
    1.10 +        and     Lawrence C Paulson, Cambridge University Computer Laboratory
    1.11      Copyright   1994 Universita' di Firenze
    1.12      Copyright   1993  University of Cambridge
    1.13  *)
    1.14  
    1.15  Relation = Prod +
    1.16  consts
    1.17 -    id	        :: "('a * 'a)set"               (*the identity relation*)
    1.18 -    O	        :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
    1.19 -    trans       :: "('a * 'a)set => bool" 	(*transitivity predicate*)
    1.20 +    id          :: "('a * 'a)set"               (*the identity relation*)
    1.21 +    O           :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
    1.22 +    trans       :: "('a * 'a)set => bool"       (*transitivity predicate*)
    1.23      converse    :: "('a * 'b)set => ('b * 'a)set"
    1.24      "^^"        :: "[('a * 'b) set, 'a set] => 'b set" (infixl 90)
    1.25      Domain      :: "('a * 'b) set => 'a set"
    1.26      Range       :: "('a * 'b) set => 'b set"
    1.27  defs
    1.28 -    id_def	"id == {p. ? x. p = (x,x)}"
    1.29 -    comp_def	"r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
    1.30 -    trans_def	  "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
    1.31 +    id_def      "id == {p. ? x. p = (x,x)}"
    1.32 +    comp_def    "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
    1.33 +    trans_def     "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
    1.34      converse_def  "converse(r) == {(y,x). (x,y):r}"
    1.35      Domain_def    "Domain(r) == {x. ? y. (x,y):r}"
    1.36      Range_def     "Range(r) == Domain(converse(r))"