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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>, <font color="Maroon">c<sub>3</sub></font> be   <a href="glib_002.html#NM1">Component</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:43_1"/><i><font color="Green">E27</font></i>: 
 <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><b>then </b> <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K22">.edgesBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="glib_002.html#E26"><i><font color="Green">Lemma25</font></i></a></i>
<br/>.= 
 <a href="glib_000.html#K26">the_Edges_of</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="glib_002.html#E26"><i><font color="Green">Lemma25</font></i></a></i>
;<br/><b>hence </b><a NAME="E3:43_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_000.html#R5">==</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:43_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="glib_000.html#T89">GLIB_000:89</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:43"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_000.html#R5">==</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>hence </b><a NAME="E3:43"/>
 <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K25">the_Vertices_of</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="glib_000.html#D36">GLIB_000:def 36</a></i>;<br/>


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