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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:162_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v</font> <a href="glib_000.html#K37" title="GLIB_000:func.37">.inNeighbors()</a> 
 ;<br/><b>then consider </b><font color="Maroon" title="c4">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:162_1"/><i><font color="Green" title="E65">A1</font></i>: 
( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> &amp; <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a>  &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/><b>take </b><font color="Maroon" title="c5">e</font> = <font color="Maroon" title="c4">e</font>;<br/><a NAME="E4:162_1"/>
( <font color="Maroon" title="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E3:162_1"><i><font color="Green" title="E65">A1</font></i></a>, <a class="txt" href="glib_000.html#E50"><i><font color="Green" title="E31">Lm8</font></i></a></i>;<br/><b>hence </b><a NAME="E5:162_1"/>
<font color="Maroon" title="c5">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_000.html#E3:162_1"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="glib_000.html#D16" target="_self" title="GLIB_000:def.16">Def16</a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon" title="c4">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><a NAME="E3:162"/><i><font color="Green" title="E65">A2</font></i>: 
<font color="Maroon" title="c4">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c1">G</font>
 ;<br/>

<a NAME="E4:162"/><i><font color="Green" title="E66">A3</font></i>: 
( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> )
 
<b>by </b><i><a class="txt" href="glib_000.html#E3:162"><i><font color="Green" title="E65">A2</font></i></a>, <a class="ref" href="glib_000.html#D16" target="_self" title="GLIB_000:def.16">Def16</a></i>;<br/>
<a NAME="E5:162"/><b>then </b><i><font color="Green" title="E67">A4</font></i>: 
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> 
 
<b>by </b><i><a class="txt" href="glib_000.html#E50"><i><font color="Green" title="E31">Lm8</font></i></a></i>;<br/>
<a NAME="E6:162"/>
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span>
 
<b>by </b><i><a class="txt" href="glib_000.html#E4:162"><i><font color="Green" title="E66">A3</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:162"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v</font> <a href="glib_000.html#K37" title="GLIB_000:func.37">.inNeighbors()</a> 
 <b>by </b><i><a class="txt" href="glib_000.html#E4:162"><i><font color="Green" title="E66">A3</font></i></a>, <a class="txt" href="glib_000.html#E5:162"><i><font color="Green" title="E67">A4</font></i></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>


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