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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_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="E1:135_1_1_1_1"/>
( <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> or  not <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:135_1_1_1_1_1"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon" title="c4">EL</font> = <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c3">x</font></span>)</span>;<br/><a NAME="E2:135_1_1_1_1_1"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 ;<br/><a NAME="E3:135_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E21">A2</font></i>: 
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <font color="Maroon" title="c1">G</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <font color="Maroon" title="c1">G</font></span>)</span>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 <b>by </b><i><a class="ref" href="partfun1.html#T25" title="PARTFUN1:th.25">PARTFUN1:25</a></i>;<br/><a NAME="E4:135_1_1_1_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_003.html#E13"><i><font color="Green" title="E6">Lm2</font></i></a></i>;<br/><a NAME="E5:135_1_1_1_1_1"/><b>then </b>
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <font color="Maroon" title="c1">G</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 <b>by </b><i><a class="txt" href="glib_003.html#E3:135_1_1_1_1_1"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="partfun1.html#T28" title="PARTFUN1:th.28">PARTFUN1:28</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c5">EL</font> = <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c3">x</font></span>)</span> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="txt" href="glib_003.html#E1:135_1_1_1_1_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="glib_003.html#E25"><i><font color="Green" title="E17">Lm4</font></i></a></i>;<br/><a NAME="E7:135_1_1_1_1_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_003.html#K13" title="GLIB_003:func.13">.labelVertex</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c5">EL</font>
 <b>by </b><i><a class="txt" href="glib_003.html#E1:135_1_1_1_1_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="glib_003.html#D22" target="_self" title="GLIB_003:def.22">Def22</a></i>;<br/><b>hence </b><a NAME="E8:135_1_1_1_1_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_003.html#K13" title="GLIB_003:func.13">.labelVertex</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">x</font> is <a href="glib_003.html#V10" title="GLIB_003:attr.10">real-vlabeled</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="135_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:135_1_1_1_1_2"/>
not <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:135_1_1_1_1_2"/>
<font color="Maroon" title="c1">G</font> <a href="glib_003.html#K13" title="GLIB_003:func.13">.labelVertex</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">x</font> is <a href="glib_003.html#V10" title="GLIB_003:attr.10">real-vlabeled</a>
 <b>by </b><i><a class="ref" href="glib_003.html#D22" target="_self" title="GLIB_003:def.22">Def22</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:135_1_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_003.html#K13" title="GLIB_003:func.13">.labelVertex</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">x</font> is <a href="glib_003.html#V10" title="GLIB_003:attr.10">real-vlabeled</a>
 ;<br/>


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