src/ZF/Cardinal.thy
author paulson
Fri, 16 Feb 1996 18:00:47 +0100
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Elimination of fully-functorial style. Type tactic changed to a type abbrevation (from a datatype). Constructor tactic and function apply deleted.
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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