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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: GLIB_005:12</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#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">EL</font> being   <a href="glib_005.html#NM1" title="GLIB_005:NM.1">FF:ELabeling</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">source</font>, <font color="Olive" title="b4">sink</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b5">V</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Olive" title="b1">G</font></span>)</span>  st <font color="Olive" title="b2">EL</font> <a href="glib_005.html#R1" title="GLIB_005:pred.1">has_valid_flow_from</a> <font color="Olive" title="b3">source</font>,<font color="Olive" title="b4">sink</font> &amp; <font color="Olive" title="b3">source</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">V</font> &amp;  not <font color="Olive" title="b4">sink</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">V</font> holds <br/><font color="Olive" title="b2">EL</font> <a href="glib_005.html#K1" title="GLIB_005:func.1">.flow</a> (<font color="Olive" title="b3">source</font>,<font color="Olive" title="b4">sink</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="uproots.html#K2" title="UPROOTS:func.2">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">G</font> <a href="glib_000.html#K23" title="GLIB_000:func.23">.edgesDBetween</a> (<font color="Olive" title="b5">V</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Olive" title="b5">V</font></span>)</span>)</span>)</span></span>)</span></div></div>
