src/HOL/Relation.thy

-(*  Title: 	Relation.thy
+(*  Title:      Relation.thy
     ID:         $Id$
-    Author: 	Riccardo Mattolini, Dip. Sistemi e Informatica
-        and	Lawrence C Paulson, Cambridge University Computer Laboratory
+    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*)
+    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)"
+    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