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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="card_5.html#NM1">Aleph</a>;<br/>

<b>assume </b><a NAME="E1:74"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="card_fil.html#V7" target="_self">measurable</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="card_fil.html#M1" target="_self">Filter</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:74"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="card_fil.html#NR3" target="_self">is_complete_with</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:74"/><i><font color="Green">E48</font></i>: 
( not <font color="Maroon">c<sub>2</sub></font> is <a href="card_fil.html#V2" target="_self">principal</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="card_fil.html#V3" target="_self">being_ultrafilter</a> )
 <b>by </b><i><a class="ref" href="card_fil.html#D16" target="_self">Def16</a></i>;<br/>
<a NAME="E5:74"/>
<font color="Maroon">c<sub>2</sub></font> <a href="card_fil.html#NR3" target="_self">is_complete_with</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="card_fil.html#E3:74"><i><font color="Green">E47</font></i></a>, <a class="ref" href="card_1.html#D5">CARD_1:def 5</a></i>;<br/>
<a NAME="E6:74"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="card_fil.html#V1" target="_self">uniform</a>
 
<b>by </b><i><a class="txt" href="card_fil.html#E4:74"><i><font color="Green">E48</font></i></a>, <a class="ref" href="card_fil.html#T23" target="_self">Th23</a></i>;<br/>
<b>assume </b><a NAME="E7:74"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="card_1.html#V2">limit</a>
 ;<br/>

<b>hence </b><a NAME="E8:74"/>
contradiction
 <b>by </b><i><a class="txt" href="card_fil.html#E3:74"><i><font color="Green">E47</font></i></a>, <a class="txt" href="card_fil.html#E4:74"><i><font color="Green">E48</font></i></a>, <a class="txt" href="card_fil.html#E6:74"><i><font color="Green">E49</font></i></a>, <a class="ref" href="card_fil.html#T37" target="_self">Th37</a></i>;<br/>


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