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<b>let </b><font color="Maroon">G</font> be   <a href="glib_003.html#NM2">EGraph</a>;<br/><b>let </b><font color="Maroon">e1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">e2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">val</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>set </b><font color="Maroon">Gn</font> = <font color="Maroon">G</font> <a href="glib_003.html#K12" target="_self">.labelEdge</a> <font color="Maroon">e1</font>,<font color="Maroon">val</font>;<br/>
<b>assume </b><a NAME="E1:192"/><i><font color="Green">E30</font></i>: 
( not <font color="Maroon">e2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_003.html#K11" target="_self">.labeledE()</a>  &amp; <font color="Maroon">e2</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_003.html#K12" target="_self">.labelEdge</a> <font color="Maroon">e1</font>,<font color="Maroon">val</font></span>)</span> <a href="glib_003.html#K11" target="_self">.labeledE()</a>  )
 ;<br/>

<a NAME="E2:192"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">e1</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:192"/><i><font color="Green">E51</font></i>: 
( not <font color="Maroon">e2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K6" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> &amp; <font color="Maroon">e2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K6" target="_self">the_ELabel_of</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="glib_003.html#K12" target="_self">.labelEdge</a> <font color="Maroon">e1</font>,<font color="Maroon">val</font></span>)</span></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:192"/>
 <a href="glib_003.html#K6" target="_self">the_ELabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_003.html#K12" target="_self">.labelEdge</a> <font color="Maroon">e1</font>,<font color="Maroon">val</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K6" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">e1</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">val</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:192"/><b>then </b>
( <font color="Maroon">e2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K6" target="_self">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> or <font color="Maroon">e2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">e1</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">val</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="funct_4.html#T13">FUNCT_4:13</a></i>;<br/>
<a NAME="E6:192"/><b>then </b>
<font color="Maroon">e2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">e1</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a>, </i>;<br/>
<b>hence </b><a NAME="E7:192"/>
<font color="Maroon">e1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e2</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>

<b>thus </b><a NAME="E8:192"/>
<font color="Maroon">e1</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font>
 <b>by </b><i>, </i>;<br/>


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