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<b>let </b><font color="Maroon">f1</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">f2</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:17_1_2"/><i><font color="Green">E46</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">BL</font> &amp; ( for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">BL</font> holds  <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</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>  &amp; <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> ) </span>}</span>  ) )
 <b>and </b><br/><a NAME="E2:17_1_2"/><i><font color="Green">E51</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">BL</font> &amp; ( for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">BL</font> holds  <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</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>  &amp; <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> ) </span>}</span>  ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:17_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">BL</font>
 ;<br/><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">BL</font> ;<br/><b>thus </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</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>  &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> ) </span>}</span> 
<b>by </b><i/>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="lopclset.html#T2" target="_self">Th2</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:17_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i>, <a class="ref" href="lopclset.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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