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

<b>let </b><font color="Maroon">w</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">t</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">s</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">t</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">s</font>
 ;<br/>

<a NAME="E2:12"/><b>then </b>
( <font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">t</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">s</font> &amp; <font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">t</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">s</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/>
<b>then consider </b><font color="Maroon">a</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E4:12"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">t</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="trees_1.html#T8">TREES_1:8</a></i>;<br/>
<a NAME="E5:12"/>
<span class="p1">(<span class="default"><font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">t</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w</font> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<a NAME="E6:12"/><b>then </b>
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/>
<a NAME="E7:12"/><b>then </b>
<font color="Maroon">t</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">s</font>
 
<b>by </b><i><a class="ref" href="trees_1.html#T8">TREES_1:8</a></i>;<br/>
<b>hence </b><a NAME="E8:12"/>
<font color="Maroon">t</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">s</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/>


</div>
