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

<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">V2G</font> =  <a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font>;<br/>
<b>set </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1;<br/>
<b>set </b><font color="Maroon">H</font> = <font color="Maroon">G</font> <a href="glib_000.html#K13">.set</a> <a href="lexbfs.html#K5" target="_self">V2LabelSelector</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1</span>)</span>;<br/>
<a NAME="E1:183_1_1"/><i><font color="Green">E34</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:183_1_1"/><i><font color="Green">E36</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:183_1_1"/>
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1 is   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1</span>)</span>, <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1</span>)</span>
 
<b>by </b><i><a class="ref" href="partfun1.html#T24">PARTFUN1:24</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">g</font> = <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1 as   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>, <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <b>by </b><i>, <a class="ref" href="partfun1.html#T28">PARTFUN1:28</a></i>;<br/>
<a NAME="E5:183_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K13">.set</a> <a href="lexbfs.html#K5" target="_self">V2LabelSelector</a> ,<font color="Maroon">g</font> is <a href="lexbfs.html#V4" target="_self">[V2Labeled]</a>
 
;<br/>
<b>reconsider </b><font color="Maroon">H</font> = <font color="Maroon">G</font> <a href="glib_000.html#K13">.set</a> <a href="lexbfs.html#K5" target="_self">V2LabelSelector</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> as  <a href="glib_000.html#V2">finite</a> <a href="lexbfs.html#NM3">VVGraph</a> <b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">V2</font> =  <a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font>;<br/>
<a NAME="E7:183_1_1"/><i><font color="Green">E39</font></i>: 
 <a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T11">GLIB_000:11</a></i>;<br/>
<a NAME="E8:183_1_1"/><i><font color="Green">E40</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<div><i><font color="Green">E42</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="183_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:183_1_1_1"/><i><font color="Green">E45</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</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>
 ;<br/><a NAME="E2:183_1_1_1"/><i><font color="Green">E46</font></i>: 
 <a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1
 <b>by </b><i><a class="ref" href="glib_000.html#T11">GLIB_000:11</a></i>;<br/><a NAME="E3:183_1_1_1"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</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>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E4:183_1_1_1"/>
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E47</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="183_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:183_1_1_2"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span>
 ;<br/><a NAME="E2:183_1_1_2"/><i><font color="Green">E49</font></i>: 
 <a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1
 <b>by </b><i><a class="ref" href="glib_000.html#T11">GLIB_000:11</a></i>;<br/><a NAME="E3:183_1_1_2"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</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>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E4:183_1_1_2"/>
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E50</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="183_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:183_1_1_3"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</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> )
 <b>and </b><br/><a NAME="E2:183_1_1_3"/><i><font color="Green">E89</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span>
 ;<br/><a NAME="E3:183_1_1_3"/><i><font color="Green">E90</font></i>: 
 <a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1
 <b>by </b><i><a class="ref" href="glib_000.html#T11">GLIB_000:11</a></i>;<br/><a NAME="E4:183_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</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>
 <b>by </b><i>, <a class="ref" href="lexbfs.html#D6" target="_self">Def6</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E5:183_1_1_3"/>
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="183_1_1_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:183_1_1_4"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font></span>)</span>
 ;<br/><b>consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:183_1_1_4"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font></span>)</span>
 <b>and </b><br/><a NAME="E4:183_1_1_4"/><i><font color="Green">E93</font></i>: 
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="183_1_1_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:183_1_1_4_1"/>
(  not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</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> or <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span> or ( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</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; not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="183_1_1_4_1_1"><b>suppose </b></a><a NAME="E1:183_1_1_4_1_1"/><i><font color="Green">E94</font></i>: 
(  not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</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> or <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span> )
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="183_1_1_4_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="183_1_1_4_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:183_1_1_4_1_1_1_1"/>
(  not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</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> or <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="183_1_1_4_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:183_1_1_4_1_1_1_1_1"/>
not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</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>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:183_1_1_4_1_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">y</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="183_1_1_4_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:183_1_1_4_1_1_1_1_2"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:183_1_1_4_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">y</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:183_1_1_4_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/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="183_1_1_4_1_2"><b>suppose </b></a><a NAME="E1:183_1_1_4_1_2"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</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; not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span> )
 ;<br/><div class="add"><a NAME="E2:183_1_1_4_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">y</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="lexbfs.html#D6" target="_self">Def6</a>, , </i>;<br/><b>hence </b><a NAME="E3:183_1_1_4_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E13:183_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</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="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E14:183_1_1"/><b>then </b>
 <a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">H</font> 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="E15:183_1_1"/>
<font color="Maroon">G</font> <a href="glib_000.html#K13">.set</a> <a href="lexbfs.html#K5" target="_self">V2LabelSelector</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lexbfs.html#K6" target="_self">the_V2Label_of</a> <font color="Maroon">G</font></span>)</span> <a href="lexbfs.html#K3" target="_self">.incSubset</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="chord.html#K2">.AdjacentSet</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p4">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> is  <a href="glib_000.html#V2">finite</a> <a href="lexbfs.html#V5" target="_self">natural-v2labeled</a> <a href="lexbfs.html#NM3">VVGraph</a>
 <b>by </b><i/>;<br/>


</div>
