src/HOL/Fun.thy
changeset 2912 3fac3e8d5d3e
parent 1475 7f5a4cd08209
child 4059 59c1422c9da5
--- a/src/HOL/Fun.thy	Fri Apr 04 16:27:39 1997 +0200
+++ b/src/HOL/Fun.thy	Fri Apr 04 16:33:28 1997 +0200
@@ -3,7 +3,22 @@
     Author:     Tobias Nipkow, Cambridge University Computer Laboratory
     Copyright   1994  University of Cambridge
 
-Lemmas about functions.
+Notions about functions.
 *)
 
-Fun = Set
+Fun = Set +
+
+consts
+
+  inj, surj     :: ('a => 'b) => bool                   (*inj/surjective*)
+  inj_onto      :: ['a => 'b, 'a set] => bool
+  inv           :: ('a => 'b) => ('b => 'a)
+
+defs
+
+  inj_def       "inj f          == ! x y. f(x)=f(y) --> x=y"
+  inj_onto_def  "inj_onto f A   == ! x:A. ! y:A. f(x)=f(y) --> x=y"
+  surj_def      "surj f         == ! y. ? x. y=f(x)"
+  inv_def       "inv(f::'a=>'b) == (% y. @x. f(x)=y)"
+
+end