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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <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>;<br/><b>let </b><font color="Maroon" title="c3">H</font> be   <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">W</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>;<br/>







<b>assume </b><a NAME="E1:26"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c4">W</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">S</font>
 ;<br/>

<a NAME="E2:26"/><i><font color="Green" title="E24">A2</font></i>: 
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S</font> &amp;  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <font color="Maroon" title="c2">S</font> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/>
<a NAME="E3:26"/><i><font color="Green" title="E25">A3</font></i>: 
<font color="Maroon" title="c4">W</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="txt" href="chord.html#E1:26"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/>
<a NAME="E4:26"/><i><font color="Green" title="E26">A4</font></i>: 
<font color="Maroon" title="c4">W</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">W</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="glib_001.html#T110" title="GLIB_001:th.110">GLIB_001:110</a></i>;<br/>
<a NAME="E5:26"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">W</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c3">H</font></span>)</span>
 
<b>by </b><i><a class="txt" href="chord.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="glib_000.html#T39" title="GLIB_000:th.39">GLIB_000:39</a></i>;<br/>
<a NAME="E6:26"/><b>then </b>
<font color="Maroon" title="c4">W</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="txt" href="chord.html#E2:26"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="chord.html#E4:26"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E7:26"/>
<font color="Maroon" title="c4">W</font> is    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="txt" href="chord.html#E3:26"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="glib_001.html#T171" title="GLIB_001:th.171">GLIB_001:171</a></i>;<br/>


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