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

<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">G2</font> be    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">G3</font> be    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G2</font>;<br/>





<a NAME="E1:140"/><i><font color="Green">E28</font></i>: 
(  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">G3</font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">G2</font> &amp;  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G3</font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G2</font> &amp; ( for <font color="Olive">v</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G3</font> holds <br/>( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G3</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G3</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font> ) ) )
 
<b>by </b><i/>;<br/>
<a NAME="E2:140"/><i><font color="Green">E29</font></i>: 
(  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">G2</font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G1</font> &amp;  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G2</font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> &amp; ( for <font color="Olive">v</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G2</font> holds <br/>( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font> ) ) )
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="140_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:140_1"/>
 <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">G3</font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G1</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><b>thus </b><a NAME="E2:140_1"/>
 <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G3</font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E3:140_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G3</font>
 ;<br/><b>hence </b><span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G3</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_000.html#D23" target="_self">Def23</a>, </i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G3</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_000.html#D23" target="_self">Def23</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i><a class="ref" href="glib_000.html#D23" target="_self">Def23</a>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:140"/>
<font color="Maroon">G3</font> is    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G1</font>
 <b>by </b><i/>;<br/>


</div>
