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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">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">v</font> is <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a> holds <br/> not <font color="Maroon" title="c1">G</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a></span><br/><b>let </b><font color="Maroon" title="c2">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</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">v</font> is <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a> implies  not <font color="Maroon" title="c1">G</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> )</span><br/>



<b>assume </b><a NAME="E1:74"/><i><font color="Green" title="E44">A1</font></i>: 
<font color="Maroon" title="c2">v</font> is <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c1">G</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:74_1"/>
<font color="Maroon" title="c1">G</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><b>then reconsider </b><font color="Maroon" title="c3">G'</font> = <font color="Maroon" title="c1">G</font> as  <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> ;<br/><a NAME="E3:74_1"/><i><font color="Green" title="E45">A2</font></i>: 
<font color="Maroon" title="c3">G'</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_002.html#E30"><i><font color="Green" title="E29">Lm18</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c4">G2</font> being   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c3">G'</font>,<font color="Maroon" title="c2">v</font>;<br/><a NAME="E5:74_1"/>
<font color="Maroon" title="c4">G2</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_002.html#E30"><i><font color="Green" title="E29">Lm18</font></i></a></i>;<br/><a NAME="E6:74_1"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 1
 <b>by </b><i><a class="txt" href="#E1:74"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="#E3:74_1"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="glib_002.html#D10" target="_self" title="GLIB_002:def.10">Def10</a></i>;<br/><b>hence </b><a NAME="E7:74_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:74"/>
not <font color="Maroon" title="c1">G</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>
 ; <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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