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))"
```