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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="glib_003.html#V7" target="_self">real-weighted</a> <a href="glib_003.html#NM1">WGraph</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7">.append</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>assume </b><a NAME="E1:171"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_001.html#K3">.first()</a> 
 ;<br/>

<a NAME="E2:171"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7">.append</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_003.html#K9" target="_self">.weightSeq()</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="glib_003.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E3:171"/><b>then </b>
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7">.append</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T105">RVSUM_1:105</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7">.append</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_003.html#K10" target="_self">.cost()</a>  = 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_003.html#K10" target="_self">.cost()</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="glib_003.html#K9" target="_self">.weightSeq()</a> </span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_003.html#K10" target="_self">.cost()</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="glib_003.html#K10" target="_self">.cost()</a> </span>)</span>

;<br/><br/>


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