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





<b>assume </b><a NAME="E1:250"/><i><font color="Green">E161</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#R5">==</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> is    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:250"/><b>then </b><i><font color="Green">E162</font></i>: 
(  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D36">GLIB_000:def 36</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="txt" href="glib_001.html#E1:250"><i><font color="Green">E161</font></i></a></i>;<br/>
<a NAME="E4:250"/><i><font color="Green">E163</font></i>: 
( not  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> is <a href="abian.html#V1">even</a> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="glib_001.html#E1:250"><i><font color="Green">E161</font></i></a>, <a class="txt" href="glib_001.html#E2:250"><i><font color="Green">E162</font></i></a>, <a class="ref" href="glib_001.html#D3" target="_self">Def3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="250_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="abian.html#V1">odd</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:250_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:250_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:250"><i><font color="Green">E161</font></i></a>, <a class="ref" href="glib_001.html#D3" target="_self">Def3</a></i>;<br/><b>hence </b><a NAME="E3:250_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:250"><i><font color="Green">E161</font></i></a>, <a class="ref" href="glib_000.html#T91">GLIB_000:91</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:250"/>
<font color="Maroon">c<sub>3</sub></font> is    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="glib_001.html#E4:250"><i><font color="Green">E163</font></i></a>, <a class="ref" href="glib_001.html#D3" target="_self">Def3</a></i>;<br/>


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