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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_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:75"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="glib_002.html#V5" target="_self">cut-vertex</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:75_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="glib_000.html#V4">trivial</a>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="glib_000.html#V4">trivial</a> <a href="glib_000.html#NM2">_Graph</a> <b>by </b><i><a class="txt" href="glib_002.html#E1:75_1"><i><font color="Green">E46</font></i></a></i>;<br/><a NAME="E3:75_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="glib_002.html#K4" target="_self">.numComponents()</a>  <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_002.html#E30"><i><font color="Green">Lemma29</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="glib_000.html#NM6">removeVertex</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><a NAME="E5:75_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="glib_002.html#K4" target="_self">.numComponents()</a>  <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_002.html#E30"><i><font color="Green">Lemma29</font></i></a></i>;<br/><a NAME="E6:75_1"/><b>then </b>
1 <a href="card_1.html#NR2" target="_self">&lt;`</a> 1
 <b>by </b><i><a class="txt" href="glib_002.html#E1:75"><i><font color="Green">E45</font></i></a>, <a class="txt" href="glib_002.html#E3:75_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="glib_002.html#D10" target="_self">Def10</a></i>;<br/><b>hence </b><a NAME="E7:75_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:75"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="glib_000.html#V4">trivial</a>
 ;<br/>


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