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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>assume </b><a NAME="E1:6_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="glib_000.html#V4">trivial</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:6_1_1"/><i><font color="Green">E5</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> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#T25">GLIB_000:25</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="glib_001.html#K1">.walkOf</a> <font color="Maroon">c<sub>2</sub></font>;<br/><a NAME="E1:6_1_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="glib_002.html#E3:6_1_1"><i><font color="Green">E5</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E2:6_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="glib_001.html#K1">.walkOf</a> <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="glib_001.html#T14">GLIB_001:14</a></i>;<br/><b>hence </b><a NAME="E3:6_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:6_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="glib_002.html#V1" target="_self">connected</a>
 <b>by </b><i><a class="ref" href="glib_002.html#D1" target="_self">Def1</a></i>;<br/>


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