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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <font color="Olive" title="b1">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> iff <font color="Olive" title="b1">W</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/><b>let </b><font color="Maroon" title="c2">W</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> iff <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>



<a NAME="E1:221"/>
( <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> iff <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="glib_001.html#D26" target="_self" title="GLIB_001:def.26">Def26</a></i>;<br/>
<b>hence </b><a NAME="E2:221"/>
( <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> implies <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> )</span><br/>

<b>assume </b><a NAME="E3:221"/>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a></span><br/>

<a NAME="E4:221"/><b>then </b>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T64" title="RELAT_1:th.64">RELAT_1:64</a></i>;<br/>
<a NAME="E5:221"/><b>then </b>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a></i>;<br/>
<b>hence </b><a NAME="E6:221"/>
<font color="Maroon" title="c2">W</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D26" target="_self" title="GLIB_001:def.26">Def26</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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