<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E19">Def8</font></span>   defines <a href="glib_004.html#K7" title="GLIB_004:func.7">DIJK:Step</a> <a onclick="hs(this)" href="javascript:()">GLIB_004:def 8 : <br/></a><span> 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">L</font> being   <a href="glib_004.html#NM2" title="GLIB_004:NM.2">DIJK:Labeling</a> of <font color="Olive" title="b1">G</font> holds <br/> ( (  <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <font color="Olive" title="b2">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="glib_004.html#K7" title="GLIB_004:func.7">DIJK:Step</a> <font color="Olive" title="b2">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">L</font> ) &amp; (  not  <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <font color="Olive" title="b2">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="glib_004.html#K7" title="GLIB_004:func.7">DIJK:Step</a> <font color="Olive" title="b2">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">L</font> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a>  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <font color="Olive" title="b2">L</font></span>)</span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Olive" title="b2">L</font> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a>  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <font color="Olive" title="b2">L</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><span class="p0">(<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="funct_1.html#K1" title="FUNCT_1:func.1">.</a>  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <font color="Olive" title="b2">L</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">L</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <font color="Olive" title="b2">L</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) );<br/></span></div>
