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<b>let </b><font color="Maroon">G2</font> be   <a href="glib_003.html#NM8">WSubgraph</a> of <font color="Maroon">G</font>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_1_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="E1:137_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G2</font></span>)</span>
 ;<br/><a NAME="E2:137_1_1_1"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">G2</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E3:137_1_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">G2</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T99">RELAT_1:99</a></i>;<br/><a NAME="E4:137_1_1_1"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E5:137_1_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="graph_5.html#K8">Real&gt;=0</a> 
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:137_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="graph_5.html#K8">Real&gt;=0</a> 
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:137_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" target="_self">the_Weight_of</a> <font color="Maroon">G2</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="graph_5.html#K8">Real&gt;=0</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="glib_003.html#D14" target="_self">GLIB_003:def 14</a><br/>


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