(* 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 "ALL z:{z: Pow(x Un y) . z eqpoll succ(k)}.
EX! w. w:t_n & z <= w "
disjoint "x Int y = 0"
includes "t_n <= {v:Pow(x Un y). v eqpoll succ(k #+ m)}"
WO_R "well_ord(y,R)"
lnat "l:nat"
mnat "m:nat"
mpos "0<m"
Infinite "~ Finite(y)"
noLepoll "~ y lepoll {v:Pow(x). v eqpoll m}"
defines
k_def "k == succ(l)"
MM_def "MM == {v:t_n. succ(k) lepoll v Int y}"
LL_def "LL == {v Int y. v:MM}"
GG_def "GG == lam v:LL. (THE w. w:MM & v <= w) - v"
s_def "s(u) == {v:t_n. u:v & k lepoll v Int y}"
end