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<b>set </b><font color="Maroon" title="c4">GG</font> = <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>;<br/>
<b>set </b><font color="Maroon" title="c5">VLG</font> =  <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <font color="Maroon" title="c1">G</font>;<br/>
<b>set </b><font color="Maroon" title="c6">VL</font> =  <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><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></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">f</font> = <font color="Maroon" title="c2">v</font> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Maroon" title="c3">x</font>;<br/>
<a NAME="E1:62_1_1"/><i><font color="Green" title="E28">A1</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">v</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a>, <a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E2:62_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E3:62_1_1"/><b>then </b><i><font color="Green" title="E29">A2</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="txt" href="lexbfs.html#E1:62_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E4:62_1_1"/><i><font color="Green" title="E30">A3</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">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#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="seqm_3.html#D8" title="SEQM_3:def.8">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" 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="62_1_1_1_1"><b>suppose </b></a><a NAME="E1:62_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>
 ;<br/><div class="add"><a NAME="E2:62_1_1_1_1"/><b>then </b>
<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> ,<span class="p1">(<span class="default"><span class="p2">(<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="p2">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_003.html#D22" title="GLIB_003:def.22">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" 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></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="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="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Maroon" title="c3">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#T11" title="GLIB_000:th.11">GLIB_000:11</a></i>;<br/><a NAME="E4:62_1_1_1_1"/><b>then </b><i><font color="Green" title="E31">A4</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><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></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<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></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T18" title="FUNCT_4:th.18">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" title="RELAT_1:func.2">rng</a> <span class="p2">(<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></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="txt" href="lexbfs.html#E3:62_1_1"><i><font color="Green" title="E29">A2</font></i></a>, <a class="txt" href="lexbfs.html#E4:62_1_1"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/><a NAME="E6:62_1_1_1_1"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><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></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="txt" href="lexbfs.html#E4:62_1_1_1_1"><i><font color="Green" title="E31">A4</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E7:62_1_1_1_1"/><b>then </b>
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><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></span>)</span> is <a href="seqm_3.html#V6" title="SEQM_3:attr.6">natural-yielding</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#D8" title="SEQM_3:def.8">SEQM_3:def 8</a></i>;<br/><b>hence </b><a NAME="E8:62_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="lexbfs.html#V3" title="LEXBFS:attr.3">natural-vlabeled</a>
 <b>by </b><i><a class="ref" href="lexbfs.html#D7" target="_self" title="LEXBFS:def.7">Def7</a></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" 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="E2:62_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="lexbfs.html#V3" title="LEXBFS:attr.3">natural-vlabeled</a>
 <b>by </b><i><a class="ref" href="glib_003.html#D22" title="GLIB_003:def.22">GLIB_003:def 22</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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