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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K30">.adj</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:71"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> ,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="glib_000.html#T16">GLIB_000:16</a></i>;<br/>
<a NAME="E3:71"/><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K30">.adj</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="glib_001.html#E1:71"><i><font color="Green">E71</font></i></a>, <a class="ref" href="glib_000.html#T69">GLIB_000:69</a></i>;<br/>
<a NAME="E4:71"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K30">.adj</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="glib_001.html#E1:71"><i><font color="Green">E71</font></i></a>, <a class="ref" href="glib_001.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E5:71"/><i><font color="Green">E74</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K30">.adj</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="glib_001.html#K3" target="_self">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> 
 
<b>by </b><i><a class="txt" href="glib_001.html#E1:71"><i><font color="Green">E71</font></i></a>, <a class="txt" href="glib_001.html#E3:71"><i><font color="Green">E72</font></i></a>, <a class="txt" href="glib_001.html#E45"><i><font color="Green">Lemma37</font></i></a></i>;<br/>
<a NAME="E6:71"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K30">.adj</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="glib_001.html#E5:71"><i><font color="Green">E74</font></i></a>, <a class="txt" href="glib_001.html#E50"><i><font color="Green">Lemma42</font></i></a></i>;<br/>
<a NAME="E7:71"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3
 
<b>by </b><i><a class="txt" href="glib_001.html#E4:71"><i><font color="Green">E73</font></i></a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>
<b>hence </b> <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1

<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2

;<br/><br/>


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