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

<b>let </b><font color="Maroon">A1</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Maroon">A2</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>

<b>given </b><font color="Maroon">f1</font> being   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font><b> such that </b><a NAME="E1:10_1_2"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a>  <a href="kurato_2.html#K1" target="_self">Union</a> <font color="Maroon">f1</font> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f1</font> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="kurato_2.html#K2" target="_self">meet</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="kurato_2.html#K3" target="_self">^\</a> <font color="Olive">n</font></span>)</span> ) )
 ;<br/>

<b>given </b><font color="Maroon">f2</font> being   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font><b> such that </b><a NAME="E2:10_1_2"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a>  <a href="kurato_2.html#K1" target="_self">Union</a> <font color="Maroon">f2</font> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f2</font> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="kurato_2.html#K2" target="_self">meet</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="kurato_2.html#K3" target="_self">^\</a> <font color="Olive">n</font></span>)</span> ) )
 ;<br/>

<a NAME="E3:10_1_2"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f1</font> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<font color="Maroon">f1</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font> = 
 <a href="kurato_2.html#K2" target="_self">meet</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="kurato_2.html#K3" target="_self">^\</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">f2</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:10_1_2_1"/>
<font color="Maroon">f1</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">n</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:10_1_2"/>
<font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font>
 <b>by </b><i>, , </i>;<br/>


</div>
