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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: GLIB_004:12</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#V8" title="GLIB_003:attr.8">nonnegative-weighted</a>  <a href="glib_003.html#NM1" title="GLIB_003:NM.1">WGraph</a><br/>  for <font color="Olive" title="b2">W</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="b3">x</font>, <font color="Olive" title="b4">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b5">m</font>, <font color="Olive" title="b6">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b2">W</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font> holds <br/><font color="Olive" title="b2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (<font color="Olive" title="b5">m</font>,<font color="Olive" title="b6">n</font>) <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (<font color="Olive" title="b5">m</font>,<font color="Olive" title="b6">n</font>)</span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> ,<span class="p1">(<span class="default"><font color="Olive" title="b2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (<font color="Olive" title="b5">m</font>,<font color="Olive" title="b6">n</font>)</span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </div></div>
