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<b>set </b><font color="Maroon" title="c2">IT</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">W</font> where <font color="Olive" title="b1">W</font> is   <a href="glib_001.html#NM4" title="GLIB_001:NM.4">Trail</a> of <font color="Maroon" title="c1">G</font> : verum </span>}</span> ;<br/>
<a NAME="E1:139_1_1"/><i><font color="Green" title="E103">A1</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">W</font> where <font color="Olive" title="b1">W</font> is   <a href="glib_001.html#NM4" title="GLIB_001:NM.4">Trail</a> of <font color="Maroon" title="c1">G</font> : verum </span>}</span> 
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="139_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:139_1_1_1"/>
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">W</font> where <font color="Olive" title="b1">W</font> is   <a href="glib_001.html#NM4" title="GLIB_001:NM.4">Trail</a> of <font color="Maroon" title="c1">G</font> : verum </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c4">W</font> being   <a href="glib_001.html#NM4" title="GLIB_001:NM.4">Trail</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:139_1_1_1"/><i><font color="Green" title="E104">A2</font></i>: 
<font color="Maroon" title="c4">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">e</font>
 ;<br/><b>thus </b><a NAME="E4:139_1_1_1"/>
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K21" title="GLIB_001:func.21">.allWalks()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E3:139_1_1_1"><i><font color="Green" title="E104">A2</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:139_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">W</font> where <font color="Olive" title="b1">W</font> is   <a href="glib_001.html#NM4" title="GLIB_001:NM.4">Trail</a> of <font color="Maroon" title="c1">G</font> : verum </span>}</span>  is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K21" title="GLIB_001:func.21">.allWalks()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:139_1_1"><i><font color="Green" title="E103">A1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>


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