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<b>let </b><font color="Maroon">G1</font> be  <a href="glib_000.html#V2" target="_self">finite</a> <a href="glib_000.html#NM2">_Graph</a>;<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/>





<a NAME="E1:149"/><i><font color="Green">E28</font></i>: 
(  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">G2</font> &amp;  <a href="glib_000.html#K26" target="_self">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" target="_self">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#D25" target="_self">Def25</a></i>;<br/>
<b>thus </b><a NAME="E2:149"/>
<font color="Maroon">G1</font> <a href="glib_000.html#K16" target="_self">.order()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">G2</font> <a href="glib_000.html#K16" target="_self">.order()</a> 
 <b>by </b><i><a class="txt" href="glib_000.html#E30"><i><font color="Green">Lemma62</font></i></a></i>;<br/>

<b>assume </b><a NAME="E3:149"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font>
 ;<br/>

<a NAME="E4:149"/>
<font color="Maroon">e</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="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E5:149"/><b>then </b><i><font color="Green">E30</font></i>: 
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G2</font>
 
<b>by </b><i><a class="txt" href="glib_000.html#E30"><i><font color="Green">Lemma62</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E6:149"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">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> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:149"/><b>then </b>
<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> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E8:149"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G2</font></span>)</span> <a href="xboole_0.html#K2">\/</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_000.html#E30"><i><font color="Green">Lemma62</font></i></a>, <a class="ref" href="xboole_1.html#T45">XBOOLE_1:45</a></i>;<br/>
<b>thus </b><a NAME="E9:149"/>
<font color="Maroon">G1</font> <a href="glib_000.html#K18" target="_self">.size()</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="glib_000.html#K18" target="_self">.size()</a> </span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, , <a class="ref" href="card_2.html#T54">CARD_2:54</a></i>;<br/>


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