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

<b>set </b><font color="Maroon">GG</font> = <font color="Maroon">G</font> <a href="glib_003.html#K13">.labelVertex</a> <font color="Maroon">v</font>,<font color="Maroon">x</font>;<br/>
<b>set </b><font color="Maroon">VLG</font> =  <a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font>;<br/>
<b>set </b><font color="Maroon">VL</font> =  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_003.html#K13">.labelVertex</a> <font color="Maroon">v</font>,<font color="Maroon">x</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">f</font> = <font color="Maroon">v</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">x</font>;<br/>
<a NAME="E1:62_1_1"/><i><font color="Green">E34</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E2:62_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E3:62_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E4:62_1_1"/><i><font color="Green">E38</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="seqm_3.html#D8">SEQM_3:def 8</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:62_1_1_1"/>
( <font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> or  not <font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_1_1_1_1"><b>suppose </b></a><a NAME="E1:62_1_1_1_1"/>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 ;<br/><div class="add"><a NAME="E2:62_1_1_1_1"/><b>then </b>
<font color="Maroon">G</font> <a href="glib_003.html#K13">.labelVertex</a> <font color="Maroon">v</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K4">VLabelSelector</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_003.html#D22">GLIB_003:def 22</a></i>;<br/><a NAME="E3:62_1_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_003.html#K13">.labelVertex</a> <font color="Maroon">v</font>,<font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_003.html#K4">VLabelSelector</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#T11">GLIB_000:11</a></i>;<br/><a NAME="E4:62_1_1_1_1"/><b>then </b><i><font color="Green">E39</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_003.html#K13">.labelVertex</a> <font color="Maroon">v</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T18">FUNCT_4:18</a></i>;<br/><a NAME="E5:62_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/><a NAME="E6:62_1_1_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_003.html#K13">.labelVertex</a> <font color="Maroon">v</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E7:62_1_1_1_1"/><b>then </b>
 <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_003.html#K13">.labelVertex</a> <font color="Maroon">v</font>,<font color="Maroon">x</font></span>)</span> is <a href="seqm_3.html#V6">natural-yielding</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#D8">SEQM_3:def 8</a></i>;<br/><b>hence </b><a NAME="E8:62_1_1_1_1"/>
<font color="Maroon">G</font> <a href="glib_003.html#K13">.labelVertex</a> <font color="Maroon">v</font>,<font color="Maroon">x</font> is <a href="lexbfs.html#V3" target="_self">natural-vlabeled</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_1_1_1_2"><b>suppose </b></a><a NAME="E1:62_1_1_1_2"/>
not <font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:62_1_1_1_2"/>
<font color="Maroon">G</font> <a href="glib_003.html#K13">.labelVertex</a> <font color="Maroon">v</font>,<font color="Maroon">x</font> is <a href="lexbfs.html#V3" target="_self">natural-vlabeled</a>
 <b>by </b><i><a class="ref" href="glib_003.html#D22">GLIB_003:def 22</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
