<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E50">Th53</font></span>: <a NAME="T55"><span class="comment"><font color="firebrick">:: GRAPH_5:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">W</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b2">G</font> being   <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a><br/>  for <font color="Olive" title="b3">pe</font>, <font color="Olive" title="b4">qe</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b2">G</font>  st <font color="Olive" title="b4">qe</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b4">qe</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">pe</font> &amp; <font color="Olive" title="b1">W</font> <a href="graph_5.html#R5" title="GRAPH_5:pred.5">is_weight&gt;=0of</a> <font color="Olive" title="b2">G</font> holds <br/> <a href="graph_5.html#K10" title="GRAPH_5:func.10">cost</a> (<font color="Olive" title="b4">qe</font>,<font color="Olive" title="b1">W</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="graph_5.html#K10" title="GRAPH_5:func.10">cost</a> (<font color="Olive" title="b3">pe</font>,<font color="Olive" title="b1">W</font>)</div></div>
