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<b>let </b><font color="Maroon">G</font> be  <a href="glib_003.html#V8" target="_self">nonnegative-weighted</a> <a href="glib_003.html#NM1">WGraph</a>;<br/><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:176"/>
<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>
 ;<br/>

<a NAME="E2:176"/><b>then </b>
<font color="Maroon">e</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#K5" target="_self">the_Weight_of</a> <font color="Maroon">G</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E3:176"/><b>then </b><i><font color="Green">E30</font></i>: 
<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="seq_1.html#K1">.</a> <font color="Maroon">e</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><a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<a NAME="E4:176"/>
 <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/>
<a NAME="E5:176"/><b>then </b>
<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="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="graph_5.html#K8">Real&gt;=0</a> 
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">r</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E7:176"/><i><font color="Green">E32</font></i>: 
( <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="seq_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> &amp; <font color="Maroon">r</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="ref" href="graph_5.html#D12">GRAPH_5:def 12</a></i>;<br/>
<b>thus </b><a NAME="E8:176"/>
0 <a href="xxreal_0.html#R1">&lt;=</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="seq_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i/>;<br/>


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