(* Title: ZF/AC/AC16_WO4.thy
ID: $Id$
Author: Krzysztof Grabczewski
Tidied using locales by LCP
*)
AC16_WO4 = OrderType + AC16_lemmas + Cardinal_aux +
locale AC16 =
fixes
x :: i
y :: i
k :: i
l :: i
m :: i
t_n :: i
R :: i
MM :: i
LL :: i
GG :: i
s :: i=>i
assumes
all_ex "\\<forall>z \\<in> {z \\<in> Pow(x Un y) . z eqpoll succ(k)}.
\\<exists>! w. w \\<in> t_n & z \\<subseteq> w "
disjoint "x Int y = 0"
includes "t_n \\<subseteq> {v \\<in> Pow(x Un y). v eqpoll succ(k #+ m)}"
WO_R "well_ord(y,R)"
lnat "l \\<in> nat"
mnat "m \\<in> nat"
mpos "0<m"
Infinite "~ Finite(y)"
noLepoll "~ y lepoll {v \\<in> Pow(x). v eqpoll m}"
defines
k_def "k == succ(l)"
MM_def "MM == {v \\<in> t_n. succ(k) lepoll v Int y}"
LL_def "LL == {v Int y. v \\<in> MM}"
GG_def "GG == \\<lambda>v \\<in> LL. (THE w. w \\<in> MM & v \\<subseteq> w) - v"
s_def "s(u) == {v \\<in> t_n. u \\<in> v & k lepoll v Int y}"
end