<?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="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:113"/><i><font color="Green">E51</font></i>: 
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K5" target="_self">_GraphSelectors</a> 
 ;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E2:113"/><i><font color="Green">E52</font></i>: 
(  <a href="glib_000.html#K1" target="_self">VertexSelector</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="glib_000.html#K2" target="_self">EdgeSelector</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="glib_000.html#K3" target="_self">SourceSelector</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="glib_000.html#K4" target="_self">TargetSelector</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E3:113"/><i><font color="Green">E53</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T11">FUNCT_4:11</a></i>;<br/>
<a NAME="E4:113"/><i><font color="Green">E54</font></i>: 
(  <a href="glib_000.html#K1" target="_self">VertexSelector</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="glib_000.html#K2" target="_self">EdgeSelector</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="glib_000.html#K3" target="_self">SourceSelector</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="glib_000.html#K4" target="_self">TargetSelector</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="glib_000.html#E1:113"><i><font color="Green">E51</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E5:113"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E6:113"/><b>then </b>
( not  <a href="glib_000.html#K1" target="_self">VertexSelector</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; not  <a href="glib_000.html#K2" target="_self">EdgeSelector</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; not  <a href="glib_000.html#K3" target="_self">SourceSelector</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; not  <a href="glib_000.html#K4" target="_self">TargetSelector</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="glib_000.html#E4:113"><i><font color="Green">E54</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:113"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K1" target="_self">VertexSelector</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K1" target="_self">VertexSelector</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K2" target="_self">EdgeSelector</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K2" target="_self">EdgeSelector</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K3" target="_self">SourceSelector</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K3" target="_self">SourceSelector</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K4" target="_self">TargetSelector</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K4" target="_self">TargetSelector</a>  )
 
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<a NAME="E8:113"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K1" target="_self">VertexSelector</a>  <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K2" target="_self">EdgeSelector</a>  <a href="hidden.html#R1">=</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"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K3" target="_self">SourceSelector</a>  <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K4" target="_self">TargetSelector</a>  <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E9:113"/>
(  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="glib_000.html#K8" target="_self">the_Source_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="glib_000.html#K9" target="_self">the_Target_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<b>hence </b><a NAME="E10:113"/>
<font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13" target="_self">.set</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is   <a href="glib_000.html#NM2">_Graph</a>
 <b>by </b><i><a class="txt" href="glib_000.html#E2:113"><i><font color="Green">E52</font></i></a>, <a class="txt" href="glib_000.html#E3:113"><i><font color="Green">E53</font></i></a>, <a class="ref" href="glib_000.html#D11" target="_self">Def11</a></i>;<br/>


</div>
