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<b>let </b><font color="Maroon">W</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">G</font> be   <a href="graph_1.html#NM1">Graph</a>;<br/><b>let </b><font color="Maroon">pe</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="graph_1.html#U2">Edges</a> of <font color="Maroon">G</font>;<br/>





<b>assume </b><a NAME="E1:74"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">W</font> <a href="graph_5.html#R5" target="_self">is_weight&gt;=0of</a> <font color="Maroon">G</font>
 ;<br/>

<b>set </b><font color="Maroon">f</font> =  <a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">pe</font>,<font color="Maroon">W</font>;<br/>
<a NAME="E2:74"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">pe</font>,<font color="Maroon">W</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">pe</font>,<font color="Maroon">W</font></span>)</span> <a href="goboard1.html#K1">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="graph_5.html#T7" target="_self">Th7</a>, </i>;<br/>
<a NAME="E3:74"/><b>then </b>
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">pe</font>,<font color="Maroon">W</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T114">RVSUM_1:114</a></i>;<br/>
<b>hence </b><a NAME="E4:74"/>
 <a href="graph_5.html#K10" target="_self">cost</a> <font color="Maroon">pe</font>,<font color="Maroon">W</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/>


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