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