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<b>let </b><font color="Maroon" title="c1">W</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/><b>let </b><font color="Maroon" title="c2">G</font> be   <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">Graph</a>;<br/><b>let </b><font color="Maroon" title="c3">pe</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c2">G</font>;<br/>





<b>assume </b><a NAME="E1:73"/><i><font color="Green" title="E60">A1</font></i>: 
<font color="Maroon" title="c1">W</font> <a href="graph_5.html#R5" title="GRAPH_5:pred.5">is_weight&gt;=0of</a> <font color="Maroon" title="c2">G</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c4">f</font> =  <a href="graph_5.html#K9" title="GRAPH_5:func.9">RealSequence</a> <font color="Maroon" title="c3">pe</font>,<font color="Maroon" title="c1">W</font>;<br/>
<a NAME="E2:73"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="graph_5.html#K9" title="GRAPH_5:func.9">RealSequence</a> <font color="Maroon" title="c3">pe</font>,<font color="Maroon" title="c1">W</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="graph_5.html#K9" title="GRAPH_5:func.9">RealSequence</a> <font color="Maroon" title="c3">pe</font>,<font color="Maroon" title="c1">W</font></span>)</span> <a href="goboard1.html#K1" title="GOBOARD1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="graph_5.html#E1:73"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="graph_5.html#T51" target="_self" title="GRAPH_5:th.51">Th51</a></i>;<br/>
<a NAME="E3:73"/><b>then </b>
 <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><a href="graph_5.html#K9" title="GRAPH_5:func.9">RealSequence</a> <font color="Maroon" title="c3">pe</font>,<font color="Maroon" title="c1">W</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T114" title="RVSUM_1:th.114">RVSUM_1:114</a></i>;<br/>
<b>hence </b><a NAME="E4:73"/>
 <a href="graph_5.html#K10" title="GRAPH_5:func.10">cost</a> <font color="Maroon" title="c3">pe</font>,<font color="Maroon" title="c1">W</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 ;<br/>


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