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

<b>let </b><font color="Maroon">T</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>, <font color="Maroon">T'</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font>;<br/>



<a NAME="E1:106"/>
( <font color="Maroon">p</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">p</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font></span>)</span> <a href="trees_1.html#K5">with-replacement</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T'</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="trees_2.html#K8">with-replacement</a> <font color="Maroon">p</font>,<font color="Maroon">T'</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T</font></span>)</span> <a href="trees_1.html#K5">with-replacement</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T'</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="trees_1.html#D12">TREES_1:def 12</a>, <a class="ref" href="trees_2.html#D12">TREES_2:def 12</a></i>;<br/>
<b>then consider </b><font color="Maroon">r</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="E3:106"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T'</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">r</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="trees_2.html#K8">with-replacement</a> <font color="Maroon">p</font>,<font color="Maroon">T'</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T'</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">r</font> )
 <b>by </b><i><a class="ref" href="trees_2.html#D12">TREES_2:def 12</a></i>;<br/>
<a NAME="E4:106"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/>
<b>hence </b><a NAME="E5:106"/>
<span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="trees_2.html#K8">with-replacement</a> <font color="Maroon">p</font>,<font color="Maroon">T'</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T'</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="trees_3.html#D4" target="_self">Def4</a>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/>


</div>
