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<b>set </b><font color="Maroon">VL</font> = <span class="p1">(<span class="default"><a href="glib_003.html#K7" target="_self">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>;<br/>
<b>set </b><font color="Maroon">G2</font> = <font color="Maroon">G</font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K4" target="_self">VLabelSelector</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" target="_self">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>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:120_1_1_1"/><i><font color="Green">E30</font></i>: 
<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/><a NAME="E2:120_1_1_1"/><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" target="_self">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> <a href="hidden.html#R1">=</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" target="_self">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#K1">dom</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#D1">FUNCT_4:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:120_1_1_1_1"/><i><font color="Green">E51</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"><span class="p2">(<span class="default"><a href="glib_003.html#K7" target="_self">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>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_1_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_1_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="E1:120_1_1_1_1_1_1"/>
( <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" target="_self">the_VLabel_of</a> <font color="Maroon">G</font></span>)</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"><font color="Maroon">v</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">x</font></span>)</span> )
 </span><b>by </b><i>, , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:120_1_1_1_1_1_1_1"/><i><font color="Green">E52</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="glib_003.html#K7" target="_self">the_VLabel_of</a> <font color="Maroon">G</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:120_1_1_1_1_1_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" target="_self">the_VLabel_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/><b>hence </b><a NAME="E3:120_1_1_1_1_1_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:120_1_1_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"><font color="Maroon">v</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">x</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:120_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</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>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><b>hence </b><a NAME="E3:120_1_1_1_1_1_1_2"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:120_1_1_1_1"/>
<font color="Maroon">y</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><b>end;</b></div><a NAME="E4:120_1_1_1"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" target="_self">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> <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><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><a NAME="E5:120_1_1_1"/>
<span class="p1">(<span class="default"><a href="glib_003.html#K7" target="_self">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> 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="glib_003.html#K7" target="_self">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>, <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" target="_self">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="partfun1.html#T24">PARTFUN1:24</a></i>;<br/><b>then reconsider </b><font color="Maroon">V1</font> = <span class="p1">(<span class="default"><a href="glib_003.html#K7" target="_self">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> 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="glib_003.html#K7" target="_self">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="partfun1.html#T28">PARTFUN1:28</a></i>;<br/><a NAME="E7:120_1_1_1"/>
<font color="Maroon">G</font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K4" target="_self">VLabelSelector</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" target="_self">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> <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" target="_self">VLabelSelector</a> ,<font color="Maroon">V1</font>
 ;<br/><b>hence </b><a NAME="E8:120_1_1_1"/>
<font color="Maroon">G</font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K4" target="_self">VLabelSelector</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" target="_self">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> is   <a href="glib_003.html#NM3">VGraph</a>
 ;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:120_1_1"/>
( 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> implies <font color="Maroon">G</font> is   <a href="glib_003.html#NM3">VGraph</a> )
 ;<br/>


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