<?xml version="1.0"?>
<div class="add">

<b>assume </b><a NAME="E1:8_1_1"/>
 <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  is <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:8_1_1"/><b>then </b>
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="card_4.html#D1" title="CARD_4:def.1">CARD_4:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:8_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="card_1.html#T14" title="CARD_1:th.14">CARD_1:14</a>, <a class="ref" href="topgen_3.html#T30" title="TOPGEN_3:th.30">TOPGEN_3:30</a>, <a class="ref" href="topgen_3.html#D4" title="TOPGEN_3:def.4">TOPGEN_3:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
