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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>set </b><font color="Maroon" title="c3">G1</font> = <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> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ;<br/>
<b>set </b><font color="Maroon" title="c4">g</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ;<br/>
<a NAME="E1:191"/><i><font color="Green" title="E105">A1</font></i>: 
<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> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="glib_003.html#T8" title="GLIB_003:th.8">GLIB_003:8</a></i>;<br/>
<a NAME="E2:191"/><i><font color="Green" title="E106">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E3:191"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><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> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E1:191"><i><font color="Green" title="E105">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">f</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  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> <span class="p1">(<span class="default"><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> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>, <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <b>by </b><i><a class="ref" href="partfun1.html#T24" title="PARTFUN1:th.24">PARTFUN1:24</a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">G2</font> = <span class="p1">(<span class="default"><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> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="lexbfs.html#K5" title="LEXBFS:func.5">V2LabelSelector</a> ,<font color="Maroon" title="c5">f</font>;<br/>
<div><i><font color="Green" title="E107">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="191_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="191_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:191_1_1"/>
( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f</font> or  not <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="191_1_1_1"><b>suppose </b></a><a NAME="E1:191_1_1_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:191_1_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="lexbfs.html#E2:191"><i><font color="Green" title="E106">A2</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="191_1_1_2"><b>suppose </b></a><a NAME="E1:191_1_1_2"/>
not <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:191_1_1_2"/>
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="funct_1.html#D4" title="FUNCT_1:def.4">FUNCT_1:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>thus </b><a NAME="E6:191"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p2">(<span class="default"><a href="lexbfs.html#K20" title="LEXBFS:func.20">MCS:Init</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="ref" href="glib_000.html#T11" title="GLIB_000:th.11">GLIB_000:11</a>, <a class="txt" href="lexbfs.html#E2:191"><i><font color="Green" title="E106">A2</font></i></a></i>;<br/>

<a NAME="E7:191"/>
 <a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="lexbfs.html#K5" title="LEXBFS:func.5">V2LabelSelector</a> ,<font color="Maroon" title="c5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T11" title="GLIB_000:th.11">GLIB_000:11</a></i>;<br/>
<b>hence </b><a NAME="E8:191"/>
<span class="p1">(<span class="default"><a href="lexbfs.html#K6" title="LEXBFS:func.6">the_V2Label_of</a> <span class="p2">(<span class="default"><a href="lexbfs.html#K20" title="LEXBFS:func.20">MCS:Init</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="lexbfs.html#E5:191"><i><font color="Green" title="E107">A3</font></i></a></i>;<br/>


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