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

<b>let </b><font color="Maroon" title="c1">GS</font> be    <a href="glib_000.html#M1" title="GLIB_000:mode.1">GraphStruct</a> ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>now </b></a><div class="add"><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:13_1_1"/>
(  <a href="glib_000.html#K1" title="GLIB_000:func.1">VertexSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font> &amp;  <a href="glib_000.html#K2" title="GLIB_000:func.2">EdgeSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font> &amp;  <a href="glib_000.html#K3" title="GLIB_000:func.3">SourceSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font> &amp;  <a href="glib_000.html#K4" title="GLIB_000:func.4">TargetSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font> )
 ;<br/><a NAME="E2:13_1_1"/><b>then </b>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><b>hence </b><a NAME="E3:13_1_1"/>
 <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:13_1"/><i><font color="Green" title="E4">A1</font></i>: 
 <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font>
 ;<br/><a NAME="E3:13_1"/>
(  <a href="glib_000.html#K1" title="GLIB_000:func.1">VertexSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  &amp;  <a href="glib_000.html#K2" title="GLIB_000:func.2">EdgeSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  &amp;  <a href="glib_000.html#K3" title="GLIB_000:func.3">SourceSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  &amp;  <a href="glib_000.html#K4" title="GLIB_000:func.4">TargetSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  )
 <b>by </b><i><a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><b>hence </b><a NAME="E4:13_1"/>
(  <a href="glib_000.html#K1" title="GLIB_000:func.1">VertexSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font> &amp;  <a href="glib_000.html#K2" title="GLIB_000:func.2">EdgeSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font> &amp;  <a href="glib_000.html#K3" title="GLIB_000:func.3">SourceSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font> &amp;  <a href="glib_000.html#K4" title="GLIB_000:func.4">TargetSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E2:13_1"><i><font color="Green" title="E4">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:13"/>
( <font color="Maroon" title="c1">GS</font> is <a href="glib_000.html#V1" title="GLIB_000:attr.1">[Graph-like]</a> iff (  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">GS</font> &amp; not  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">GS</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="glib_000.html#K8" title="GLIB_000:func.8">the_Source_of</a> <font color="Maroon" title="c1">GS</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">GS</font>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">GS</font> &amp;  <a href="glib_000.html#K9" title="GLIB_000:func.9">the_Target_of</a> <font color="Maroon" title="c1">GS</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">GS</font>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">GS</font> ) )
 <b>by </b><i><a class="ref" href="glib_000.html#D11" target="_self" title="GLIB_000:def.11">Def11</a></i>;<br/>


</div>
