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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/>



<a NAME="E1:221"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="glib_001.html#V3" target="_self">trivial</a> iff <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K15" target="_self">.length()</a>  <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="glib_001.html#D26" target="_self">Def26</a></i>;<br/>
<a NAME="E2:221"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> is <a href="glib_001.html#V3" target="_self">trivial</a> iff  <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#K12" target="_self">.edgeSeq()</a> </span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
;<br/>
<a NAME="E3:221"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> is <a href="glib_001.html#V3" target="_self">trivial</a> iff <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<b>hence </b><a NAME="E4:221"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="glib_001.html#V3" target="_self">trivial</a> implies <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K14" target="_self">.edges()</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>;<br/>

<b>assume </b><a NAME="E5:221"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K14" target="_self">.edges()</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E6:221"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
;<br/>
<a NAME="E7:221"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T64">RELAT_1:64</a></i>;<br/>
<a NAME="E8:221"/><b>then </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#K12" target="_self">.edgeSeq()</a> </span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<a NAME="E9:221"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K15" target="_self">.length()</a>  <a href="hidden.html#R1">=</a> 0
 
;<br/>
<b>hence </b><a NAME="E10:221"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="glib_001.html#V3" target="_self">trivial</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D26" target="_self">Def26</a></i>;<br/>


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