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

<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">G2</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:248"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">G1</font> <a href="glib_000.html#R5">==</a> <font color="Maroon">G2</font> &amp; <font color="Maroon">x</font> is    <a href="glib_001.html#M1" target="_self">VertexSeq</a> of <font color="Maroon">G1</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">x2</font> = <font color="Maroon">x</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G2</font> <b>by </b><i><a class="ref" href="glib_000.html#D36">GLIB_000:def 36</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="248_1"><b>now </b></a><div class="add"><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>assume </b><a NAME="E1:248_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x2</font> )
 ;<br/><b>then consider </b><font color="Maroon">e</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:248_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">x2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>,<font color="Maroon">x2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G1</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E57"><i><font color="Green">Lemma161</font></i></a>, </i>;<br/><a NAME="E4:248_1"/>
<font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">x2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>,<font color="Maroon">x2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G2</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E57"><i><font color="Green">Lemma161</font></i></a>, , <a class="ref" href="glib_000.html#T91">GLIB_000:91</a></i>;<br/><b>hence </b><a NAME="E5:248_1"/>
 ex <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">x2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>,<font color="Maroon">x2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G2</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:248"/>
<font color="Maroon">x</font> is    <a href="glib_001.html#M1" target="_self">VertexSeq</a> of <font color="Maroon">G2</font>
 <b>by </b><i/>;<br/>


</div>
