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<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="glib_004.html#K5" target="_self">DIJK:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means <span class="p1">(<span class="default"><a href="glib_004.html#K5" target="_self">DIJK:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <font color="Maroon">a<sub>1</sub></font> is <a href="glib_000.html#V2">finite</a>;<br/>
<span class="p1">(<span class="default"><a href="glib_004.html#K5" target="_self">DIJK:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> 0 = 
 <a href="glib_004.html#K4" target="_self">DIJK:Init</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="glib_004.html#D7" target="_self">Def7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K3">ELabelSelector</a> ,<a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K4">VLabelSelector</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> 0</span>)</span>

;<br/>
<a NAME="E2:19_1_1"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
;<br/>
<div><i><font color="Green">E14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:19_1_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>4</sub></font>]
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="glib_004.html#K5" target="_self">DIJK:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <font color="Maroon">c<sub>4</sub></font> as  <a href="glib_000.html#V2">finite</a> <a href="glib_003.html#V11">real-WEV</a> <a href="glib_003.html#NM7">WEVGraph</a> ;<br/><a NAME="E3:19_1_1_2"/>
<span class="p1">(<span class="default"><a href="glib_004.html#K5" target="_self">DIJK:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="glib_004.html#K3" target="_self">DIJK:Step</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="glib_004.html#D7" target="_self">Def7</a></i>;<br/><b>hence </b><a NAME="E4:19_1_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E4:19_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="glib_004.html#E2:19_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="glib_004.html#E3:19_1_1"><i><font color="Green">E14</font></i></a>);<br/></i>
<b>hence </b><a NAME="E5:19_1_1"/>
 <a href="glib_004.html#K5" target="_self">DIJK:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="glib_000.html#V14">finite</a>
 <b>by </b><i><a class="ref" href="glib_000.html#D60">GLIB_000:def 60</a></i>;<br/>


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