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<div><span class="kw">theorem </span><a NAME="T13"><span class="comment"><font color="firebrick">:: GLIB_004:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="glib_000.html#V2" title="GLIB_000:attr.2">_finite</a>   <a href="glib_003.html#V7" title="GLIB_003:attr.7">real-weighted</a>  <a href="glib_003.html#NM1" title="GLIB_003:NM.1">WGraph</a><br/>  for <font color="Olive" title="b2">W1</font>, <font color="Olive" title="b3">W2</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b2">W1</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font> &amp; <font color="Olive" title="b3">W2</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font> holds <br/><font color="Olive" title="b2">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">W2</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> </div></div>
