<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/>

<b>thus </b><a NAME="E1:74"/>
( <font color="Maroon">G</font> is   <a href="glib_002.html#NM1">Component</a> of <font color="Maroon">G</font> implies <font color="Maroon">G</font> is <a href="glib_002.html#V1" target="_self">connected</a> )
 ;<br/>

<b>assume </b><a NAME="E2:74"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">G</font> is <a href="glib_002.html#V1" target="_self">connected</a>
 ;<br/>

<a NAME="E3:74"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">G</font> is    <a href="glib_000.html#M2">Subgraph</a> of <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T43">GLIB_000:43</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">G2</font> being  <a href="glib_002.html#V1" target="_self">connected</a>  <a href="glib_000.html#M2">Subgraph</a> of <font color="Maroon">G</font><b> such that </b><a NAME="E1:74_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">G</font> <a href="glib_000.html#R7">c&lt;</a> <font color="Maroon">G2</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:74_1_1_1"/>
(  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> <a href="xboole_0.html#R2">c&lt;</a>  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">G2</font> or  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> <a href="xboole_0.html#R2">c&lt;</a>  <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">G2</font> )
 </span><b>by </b><i>, , <a class="ref" href="glib_000.html#T101">GLIB_000:101</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_1_1_1"><b>suppose </b></a><a NAME="E1:74_1_1_1_1"/>
 <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> <a href="xboole_0.html#R2">c&lt;</a>  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">G2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:74_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="74_1_1_1_2"><b>suppose </b></a><a NAME="E1:74_1_1_1_2"/>
 <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font> <a href="xboole_0.html#R2">c&lt;</a>  <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">G2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:74_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:74_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:74"/>
<font color="Maroon">G</font> is   <a href="glib_002.html#NM1">Component</a> of <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#T43">GLIB_000:43</a>, </i>;<br/>


</div>
