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<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> ;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="glib_003.html#NM15">inducedWSubgraph</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_003.html#K11">.labeledE()</a> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<a NAME="E2:77_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a>  is  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_003.html#K11">.labeledE()</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K22">.edgesBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="glib_004.html#E59"><i><font color="Green">Lemma43</font></i></a></i>;<br/>
<a NAME="E3:77_1_1"/><b>then </b><i><font color="Green">E53</font></i>: 
 <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 
<b>by </b><i><a class="ref" href="glib_000.html#D39">GLIB_000:def 39</a></i>;<br/>
 <a href="glib_004.html#K14" target="_self">PRIM:MST</a> <font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K41">.Result()</a> 

<br/>.= 
<span class="p1">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span>

;<br/>
<a NAME="E5:77_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K42">.-&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K13" target="_self">PRIM:CompSeq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span></span>)</span> <a href="glib_003.html#K14">.labeledV()</a>  <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="glib_004.html#E68"><i><font color="Green">Lemma52</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:77_1_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="glib_000.html#V9">spanning</a>
 <b>by </b><i><a class="txt" href="glib_004.html#E3:77_1_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="glib_000.html#D35">GLIB_000:def 35</a></i>;<br/>

<b>thus </b><a NAME="E7:77_1_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="glib_002.html#V3">Tree-like</a>
 <b>by </b><i><a class="txt" href="glib_004.html#E67"><i><font color="Green">Lemma51</font></i></a></i>;<br/>


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