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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">C1</font> be   <a href="glib_002.html#NM1">Component</a> of <font color="Maroon">G</font>, <font color="Maroon">C2</font> be   <a href="glib_002.html#NM1">Component</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">v</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:45"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">C2</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">v'</font> = <font color="Maroon">v</font> as   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> ;<br/>
<a NAME="E3:45"/>
(  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">v'</font> &amp;  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">C2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">v'</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:45"/>
<font color="Maroon">C1</font> <a href="glib_000.html#R5">==</a> <font color="Maroon">C2</font>
 <b>by </b><i/>;<br/>


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