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<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="glib_005.html#K4" target="_self">AP:Step</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_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="E1:37_1_1_1_1"/>
(  <a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or (  <a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_003.html#K14">.labeledV()</a>  ) or (  <a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_003.html#K14">.labeledV()</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:37_1_1_1_1_1"/>
 <a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:37_1_1_1_1_1"/>
 <a href="glib_005.html#K4" target="_self">AP:Step</a> <font color="Maroon">c<sub>1</sub></font> is <a href="glib_000.html#V2">finite</a>
 <b>by </b><i><a class="ref" href="glib_005.html#D14" target="_self">Def14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:37_1_1_1_1_2"/>
(  <a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; not <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_003.html#K14">.labeledV()</a>  )
 ;<br/><div class="add"><a NAME="E2:37_1_1_1_1_2"/><b>then </b>
 <a href="glib_005.html#K4" target="_self">AP:Step</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_003.html#K13">.labelVertex</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D14" target="_self">Def14</a></i>;<br/><b>hence </b><a NAME="E3:37_1_1_1_1_2"/>
 <a href="glib_005.html#K4" target="_self">AP:Step</a> <font color="Maroon">c<sub>1</sub></font> is <a href="glib_000.html#V2">finite</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_3"><b>suppose </b></a><a NAME="E1:37_1_1_1_1_3"/>
(  <a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_003.html#K14">.labeledV()</a>  )
 ;<br/><div class="add"><a NAME="E2:37_1_1_1_1_3"/><b>then </b>
 <a href="glib_005.html#K4" target="_self">AP:Step</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_003.html#K13">.labelVertex</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><a href="glib_005.html#K3" target="_self">AP:NextBestEdges</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_005.html#D14" target="_self">Def14</a></i>;<br/><b>hence </b><a NAME="E3:37_1_1_1_1_3"/>
 <a href="glib_005.html#K4" target="_self">AP:Step</a> <font color="Maroon">c<sub>1</sub></font> is <a href="glib_000.html#V2">finite</a>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:37_1_1"/>
 <a href="glib_005.html#K4" target="_self">AP:Step</a> <font color="Maroon">c<sub>1</sub></font> is <a href="glib_000.html#V2">finite</a>
 ;<br/>


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