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<b>assume </b><a NAME="E1:8_1_1"/>
 <a href="numbers.html#K1">REAL</a>  is <a href="card_4.html#V1">countable</a>
 ;<br/>

<a NAME="E2:8_1_1"/><b>then </b>
 <a href="card_1.html#K1">Card</a> <a href="numbers.html#K1">REAL</a>  <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K3">alef</a> 0
 
<b>by </b><i><a class="ref" href="card_4.html#D1">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">CARD_1:14</a>, <a class="ref" href="topgen_3.html#T30">TOPGEN_3:30</a>, <a class="ref" href="topgen_3.html#D4">TOPGEN_3:def 4</a></i>;<br/>


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