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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="glib_000.html#M1" target="_self">GraphStruct</a> ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>now </b></a><div class="add"><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:14_1_1"/><i><font color="Green">E6</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> )
 ;<br/><a NAME="E2:14_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K5" target="_self">_GraphSelectors</a>  holds <br/><font color="Olive">b<sub>1</sub></font> <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="txt" href="glib_000.html#E1:14_1_1"><i><font color="Green">E6</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/><b>hence </b><a NAME="E3:14_1_1"/>
 <a href="glib_000.html#K5" target="_self">_GraphSelectors</a>  <a href="tarski.html#R1">c=</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="tarski.html#D3">TARSKI:def 3</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:14_1"/><i><font color="Green">E6</font></i>: 
 <a href="glib_000.html#K5" target="_self">_GraphSelectors</a>  <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E3:14_1"/>
(  <a href="glib_000.html#K1" target="_self">VertexSelector</a>  <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K5" target="_self">_GraphSelectors</a>  &amp;  <a href="glib_000.html#K2" target="_self">EdgeSelector</a>  <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K5" target="_self">_GraphSelectors</a>  &amp;  <a href="glib_000.html#K3" target="_self">SourceSelector</a>  <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K5" target="_self">_GraphSelectors</a>  &amp;  <a href="glib_000.html#K4" target="_self">TargetSelector</a>  <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K5" target="_self">_GraphSelectors</a>  )
 <b>by </b><i><a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/><b>hence </b><a NAME="E4:14_1"/>
(  <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="txt" href="glib_000.html#E2:14_1"><i><font color="Green">E6</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:14"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="glib_000.html#V1" target="_self">[Graph-like]</a> iff (  <a href="glib_000.html#K5" target="_self">_GraphSelectors</a>  <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp; not  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp;  <a href="glib_000.html#K8" target="_self">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font>, <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#K9" target="_self">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font>, <a href="glib_000.html#K6" target="_self">the_Vertices_of</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/>


</div>
