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<b>let </b><font color="Maroon">P</font> be    <a href="kurato_2.html#M1" target="_self">subsequence</a> of <font color="Maroon">X</font>;<br/>

<b>consider </b><font color="Maroon">A</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E2:65_1_1"/><i><font color="Green">E43</font></i>: 
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">X</font> <a href="kurato_2.html#K7" target="_self">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>
<a NAME="E3:65_1_1"/>
 ex <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>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">P</font> <a href="kurato_2.html#K7" target="_self">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Olive">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_1_1"><b>proof </b></a><div class="add">

<b>take </b>
<font color="Maroon">A</font>
;<br/>

<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/>

<b>consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E2:65_1_1_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">m</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">P</font> <a href="kurato_2.html#K7" target="_self">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="kurato_2.html#K7" target="_self">.</a> <font color="Maroon">m</font> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E3:65_1_1_1"/>
<font color="Maroon">P</font> <a href="kurato_2.html#K7" target="_self">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:65_1_1"/>
<font color="Maroon">P</font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i/>;<br/>


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