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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>, <font color="Maroon">T</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:34"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">T</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font>
 ;<br/>

<b>let </b><font color="Maroon">G2</font> be   <a href="glib_000.html#NM5">inducedSubgraph</a> of <font color="Maroon">G</font>,<font color="Maroon">S</font>;<br/>

<a NAME="E2:34"/><i><font color="Green">E33</font></i>: 
(  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">G2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font> &amp;  <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">G2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D39">GLIB_000:def 39</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:34_1_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <font color="Maroon">T</font>
 ;<br/><a NAME="E2:34_1_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <font color="Maroon">S</font>
 <b>by </b><i><a class="txt" href="chord.html#E1:34"><i><font color="Green">E30</font></i></a>, <a class="ref" href="glib_000.html#T39">GLIB_000:39</a></i>;<br/><a NAME="E3:34_1_1"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> )
 <b>by </b><i>, <a class="ref" href="glib_000.html#T34">GLIB_000:34</a></i>;<br/><a NAME="E4:34_1_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="chord.html#T2" target="_self">Th2</a>, , <a class="txt" href="chord.html#E2:34"><i><font color="Green">E33</font></i></a>, <a class="ref" href="glib_000.html#D34">GLIB_000:def 34</a></i>;<br/><b>hence </b><a NAME="E5:34_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G2</font> <a href="glib_000.html#K22">.edgesBetween</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="txt" href="chord.html#E2:34"><i><font color="Green">E33</font></i></a>, <a class="ref" href="chord.html#T2" target="_self">Th2</a>, , <a class="txt" href="chord.html#E3"><i><font color="Green">Lemma34</font></i></a>, <a class="ref" href="glib_000.html#T34">GLIB_000:34</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:34_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G2</font> <a href="glib_000.html#K22">.edgesBetween</a> <font color="Maroon">T</font>
 ;<br/><a NAME="E3:34_1"/><b>then </b><i><font color="Green">E66</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">G2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#T34">GLIB_000:34</a></i>;<br/><a NAME="E4:34_1"/><i><font color="Green">E67</font></i>: 
( <span class="p1">(<span class="default"><a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> )
 <b>by </b><i>, <a class="ref" href="glib_000.html#D34">GLIB_000:def 34</a></i>;<br/><b>thus </b><a NAME="E5:34_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <font color="Maroon">T</font>
 <b>by </b><i>, <a class="txt" href="chord.html#E2:34"><i><font color="Green">E33</font></i></a>, <a class="ref" href="glib_000.html#T34">GLIB_000:34</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:34"/>
<font color="Maroon">G2</font> <a href="glib_000.html#K22">.edgesBetween</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K22">.edgesBetween</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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