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<b>let </b><font color="Maroon" title="c3">A1</font>, <font color="Maroon" title="c4">A2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>given </b><font color="Maroon" title="c5">f1</font> being   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font><b> such that </b><a NAME="E2:10_2_2"/><i><font color="Green" title="E4">A5</font></i>: 
( <font color="Maroon" title="c3">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="kurato_2.html#K2" title="KURATO_2:func.2">meet</a> <font color="Maroon" title="c5">f1</font> &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c5">f1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Olive" title="b1">n</font></span>)</span> ) )
 ;<br/>

<b>given </b><font color="Maroon" title="c6">f2</font> being   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font><b> such that </b><a NAME="E4:10_2_2"/><i><font color="Green" title="E5">A6</font></i>: 
( <font color="Maroon" title="c4">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="kurato_2.html#K2" title="KURATO_2:func.2">meet</a> <font color="Maroon" title="c6">f2</font> &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c6">f2</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Olive" title="b1">n</font></span>)</span> ) )
 ;<br/>

<a NAME="E5:10_2_2"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c5">f1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f2</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b1">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<font color="Maroon" title="c5">f1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c7">n</font> = 
 <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c7">n</font></span>)</span>
<b>by </b><i><a class="txt" href="kurato_2.html#E2:10_2_2"><i><font color="Green" title="E4">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">f2</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c7">n</font>
<b>by </b><i><a class="txt" href="kurato_2.html#E4:10_2_2"><i><font color="Green" title="E5">A6</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E2:10_2_2_1"/>
<font color="Maroon" title="c5">f1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c7">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f2</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c7">n</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:10_2_2"/>
<font color="Maroon" title="c3">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A2</font>
 <b>by </b><i><a class="txt" href="kurato_2.html#E2:10_2_2"><i><font color="Green" title="E4">A5</font></i></a>, <a class="txt" href="kurato_2.html#E4:10_2_2"><i><font color="Green" title="E5">A6</font></i></a>, <a class="ref" href="kurato_2.html#T3" target="_self" title="KURATO_2:th.3">Th3</a></i>;<br/>


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