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

<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> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:153_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> 
 ;<br/><a NAME="E2:153_1"/><b>then </b><i><font color="Green">E63</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E53"><i><font color="Green">Lemma34</font></i></a></i>;<br/><b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>;<br/><b>take </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>;<br/><b>thus </b><a NAME="E3:153_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_000.html#R2" target="_self">DJoins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="glib_000.html#E2:153_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="glib_000.html#D16" target="_self">Def16</a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">c<sub>4</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E2:153"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="glib_000.html#R2" target="_self">DJoins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:153"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="glib_000.html#E2:153"><i><font color="Green">E63</font></i></a>, <a class="ref" href="glib_000.html#D16" target="_self">Def16</a></i>;<br/>
<b>hence </b><a NAME="E4:153"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> 
 <b>by </b><i><a class="txt" href="glib_000.html#E53"><i><font color="Green">Lemma34</font></i></a></i>;<br/>


</div>
