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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">W1</font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">W2</font> be    <a href="glib_001.html#M4">Subwalk</a> of <font color="Maroon">W1</font>;<br/>





<b>consider </b><font color="Maroon">ws</font> being    <a href="graph_2.html#M1">FinSubsequence</a> of <font color="Maroon">W1</font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> <b> such that </b><br/><a NAME="E2:175"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">W2</font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a>  <a href="hidden.html#R1">=</a>  <a href="glib_003.html#K1" target="_self">Seq</a> <font color="Maroon">ws</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">ws'</font> = <font color="Maroon">ws</font> as    <a href="graph_2.html#M1">FinSubsequence</a> of <font color="Maroon">W1</font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a>  ;<br/>
<a NAME="E4:175"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M2">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"><font color="Maroon">W1</font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span> holds <br/>0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">i</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:175"/><b>then </b>
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">W2</font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:175"/><b>then </b>
<font color="Maroon">W2</font> <a href="glib_003.html#K10" target="_self">.cost()</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span>
 
;<br/>
<b>hence </b><a NAME="E7:175"/>
<font color="Maroon">W2</font> <a href="glib_003.html#K10" target="_self">.cost()</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">W1</font> <a href="glib_003.html#K10" target="_self">.cost()</a> 
 ;<br/>


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