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<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">G2</font> be   <a href="glib_000.html#NM8">removeEdge</a> of <font color="Maroon">G1</font>,<font color="Maroon">e</font>;<br/>







<b>assume </b><a NAME="E1:243"/><i><font color="Green">E39</font></i>: 
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 ;<br/>

<a NAME="E2:243"/><i><font color="Green">E40</font></i>: 
(  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">G2</font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G1</font> &amp;  <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">G2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G1</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">e</font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="glib_000.html#T56">GLIB_000:56</a></i>;<br/>
<a NAME="E3:243"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">W</font> <a href="glib_001.html#K13" target="_self">.vertices()</a>  <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">G2</font>
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="243_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:243_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 ;<br/><a NAME="E2:243_1"/><b>then </b>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">e</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_001.html#E55"><i><font color="Green">Lemma158</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:243_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">G2</font>
 <b>by </b><i>, <a class="txt" href="glib_001.html#E57"><i><font color="Green">Lemma161</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:243"/><b>then </b>
<font color="Maroon">W</font> <a href="glib_001.html#K14" target="_self">.edges()</a>  <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">G2</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:243"/>
<font color="Maroon">W</font> is    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G2</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E54"><i><font color="Green">Lemma157</font></i></a>, <a class="txt" href="glib_001.html#E56"><i><font color="Green">Lemma160</font></i></a></i>;<br/>


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