src/ZF/Cardinal.thy
author lcp
Fri, 23 Dec 1994 16:32:39 +0100
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Added Krzysztof's constants lesspoll and Finite
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(*  Title: 	ZF/Cardinal.thy
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    ID:         $Id$
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    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1994  University of Cambridge
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Cardinals in Zermelo-Fraenkel Set Theory 
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*)
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Cardinal = OrderType + Fixedpt + Nat + Sum + 
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consts
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  Least            :: "(i=>o) => i"    (binder "LEAST " 10)
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  eqpoll, lepoll,
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          lesspoll :: "[i,i] => o"     (infixl 50)
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  cardinal         :: "i=>i"           ("|_|")
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  Finite, Card     :: "i=>o"
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defs
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  (*least ordinal operator*)
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  Least_def     "Least(P) == THE i. Ord(i) & P(i) & (ALL j. j<i --> ~P(j))"
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  eqpoll_def    "A eqpoll B == EX f. f: bij(A,B)"
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  lepoll_def    "A lepoll B == EX f. f: inj(A,B)"
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  lesspoll_def  "A lesspoll B == A lepoll B & ~(A eqpoll B)"
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  Finite_def    "Finite(A) == EX n:nat. A eqpoll n"
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  cardinal_def  "|A| == LEAST i. i eqpoll A"
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  Card_def      "Card(i) == (i = |i|)"
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end