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(* Title: ZF/CardinalArith.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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Cardinal Arithmetic
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*)
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516
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CardinalArith = Cardinal + OrderArith + Arith + Finite +
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437
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consts
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467
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437
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InfCard :: "i=>o"
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"|*|" :: "[i,i]=>i" (infixl 70)
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"|+|" :: "[i,i]=>i" (infixl 65)
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csquare_rel :: "i=>i"
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484
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jump_cardinal :: "i=>i"
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csucc :: "i=>i"
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437
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rules
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InfCard_def "InfCard(i) == Card(i) & nat le i"
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cadd_def "i |+| j == | i+j |"
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cmult_def "i |*| j == | i*j |"
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csquare_rel_def
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"csquare_rel(k) == rvimage(k*k, lam z:k*k. split(%x y. <x Un y, <x,y>>, z), \
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\ rmult(k,Memrel(k), k*k, \
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\ rmult(k,Memrel(k), k,Memrel(k))))"
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484
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(*This def is more complex than Kunen's but it more easily proved to
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be a cardinal*)
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jump_cardinal_def
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"jump_cardinal(K) == \
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\ UN X:Pow(K). {z. r: Pow(K*K), well_ord(X,r) & z = ordertype(X,r)}"
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(*needed because jump_cardinal(K) might not be the successor of K*)
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csucc_def "csucc(K) == LEAST L. Card(L) & K<L"
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437
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end
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