<?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/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>thus </b><a NAME="E1:73_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_002.html#K3" target="_self">.componentSet()</a> </span>)</span> implies <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> )
 ;<br/><b>assume </b><a NAME="E2:73_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 ;<br/><b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> ;<br/><b>set </b><font color="Maroon">Y</font> = <font color="Maroon">G</font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">x'</font>;<br/><a NAME="E4:73_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">x'</font>
 <b>by </b><i/>;<br/><a NAME="E5:73_1"/>
<font color="Maroon">G</font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">x'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_002.html#K3" target="_self">.componentSet()</a> 
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:73_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_002.html#K3" target="_self">.componentSet()</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:73"/>
 <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_002.html#K3" target="_self">.componentSet()</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div>
