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

<b>set </b><font color="Maroon">US</font> = <span class="p1">{<span class="default"> <font color="Olive">F</font> where <font color="Olive">F</font> is    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">BL</font> : <font color="Olive">F</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  </span>}</span> ;<br/>
<a NAME="E1:14_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive">F</font> where <font color="Olive">F</font> is    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">BL</font> : <font color="Olive">F</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">BL</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:14_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">F</font> where <font color="Olive">F</font> is    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">BL</font> : <font color="Olive">F</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">UF</font> being    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">BL</font><b> such that </b><br/><a NAME="E3:14_1_1_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">UF</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">UF</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  )
 ;<br/>
<b>thus </b><a NAME="E4:14_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">BL</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:14_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive">F</font> where <font color="Olive">F</font> is    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">BL</font> : <font color="Olive">F</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  </span>}</span>  is   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">BL</font>
 ;<br/>


</div>
