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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th8</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: GLIB_005:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <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> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b5">v</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b5">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K5" title="GLIB_005:func.5">AP:CompSeq</a> (<font color="Olive" title="b2">EL</font>,<font color="Olive" title="b3">source</font>)</span>)</span> <a href="glib_005.html#K4" title="GLIB_005:func.4">.</a> <font color="Olive" title="b4">n</font></span>)</span> holds <br/> ex <font color="Olive" title="b6">P</font> being   <a href="glib_001.html#NM5" title="GLIB_001:NM.5">Path</a> of <font color="Olive" title="b1">G</font> st <br/>( <font color="Olive" title="b6">P</font> <a href="glib_005.html#R5" title="GLIB_005:pred.5">is_augmenting_wrt</a> <font color="Olive" title="b2">EL</font> &amp; <font color="Olive" title="b6">P</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Olive" title="b3">source</font>,<font color="Olive" title="b5">v</font> &amp; <font color="Olive" title="b6">P</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K5" title="GLIB_005:func.5">AP:CompSeq</a> (<font color="Olive" title="b2">EL</font>,<font color="Olive" title="b3">source</font>)</span>)</span> <a href="glib_005.html#K4" title="GLIB_005:func.4">.</a> <font color="Olive" title="b4">n</font></span>)</span> )</div></div>
