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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">W</font> being   <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G</font> st <font color="Olive">W</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">v</font>,<font color="Maroon">a<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">IT</font> being   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span><b> such that </b><br/><a NAME="E2:16_1_1"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) )
 <b>from </b><i><a class="ref" href="subset_1.html#S1">SUBSET_1:sch 1</a>();<br/></i>
<a NAME="E3:16_1_1"/>
<font color="Maroon">G</font> <a href="glib_001.html#K1">.walkOf</a> <font color="Maroon">v</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">v</font>,<font color="Maroon">v</font>
 
<b>by </b><i><a class="ref" href="glib_001.html#T14">GLIB_001:14</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">IT</font> = <font color="Maroon">IT</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">IT</font>
;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E5:16_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> implies  ex <font color="Olive">W</font> being   <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G</font> st <font color="Olive">W</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">v</font>,<font color="Maroon">x</font> )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E6:16_1_1"/>
 ex <font color="Olive">W</font> being   <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G</font> st <font color="Olive">W</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">v</font>,<font color="Maroon">x</font>
 ;<br/>

<b>then consider </b><font color="Maroon">W</font> being    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E8:16_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">W</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">v</font>,<font color="Maroon">x</font>
 ;<br/>
<a NAME="E9:16_1_1"/>
<font color="Maroon">x</font> is   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>
 
<b>by </b><i>, <a class="ref" href="glib_001.html#T19">GLIB_001:19</a></i>;<br/>
<b>hence </b><a NAME="E10:16_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 <b>by </b><i>, </i>;<br/>


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