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

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="trees_1.html#K5">with-replacement</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D14" target="_self">TREES_3:def 14</a><br/>

<b>assume </b><a NAME="E1:99_1_1"/><i><font color="Green">E43</font></i>: 
not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:99_1_1"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="trees_1.html#D12">TREES_1:def 12</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<a NAME="E4:99_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/>
<a NAME="E5:99_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="trees_3.html#E1:99_1_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="trees_3.html#E3:99_1_1"><i><font color="Green">E44</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:99_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="trees_3.html#E3:99_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="trees_1.html#T33">TREES_1:33</a></i>;<br/>


</div>
