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<b>let </b><font color="Maroon">G</font> be   <a href="graph_1.html#NM1">Graph</a>;<br/><b>let </b><font color="Maroon">H1</font> be  <a href="graph_1.html#V1" target="_self">strict</a>  <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">G</font>, <font color="Maroon">H2</font> be  <a href="graph_1.html#V1" target="_self">strict</a>  <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:38"/><i><font color="Green">E29</font></i>: 
( the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H2</font> &amp; the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H2</font> )
 ;<br/>

<a NAME="E2:38"/><i><font color="Green">E35</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:38"/><i><font color="Green">E36</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">H2</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:38"/><i><font color="Green">E37</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:38"/><i><font color="Green">E38</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">H2</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:38"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H1</font> holds <br/>the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">H1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">H2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:38_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H1</font>
 ;<br/>

<b>hence </b>the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">H1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">H2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , </i>
;<br/><br/>


</div><b>end;</b></div>
<a NAME="E7:38"/><b>then </b><i><font color="Green">E40</font></i>: 
the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">H2</font>
 
<b>by </b><i>, <a class="ref" href="graph_1.html#D1" target="_self">Def1</a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>
<a NAME="E8:38"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H1</font> holds <br/>the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">H1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">H2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:38_2"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H1</font>
 ;<br/>

<b>hence </b>the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">H1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">H2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="txt" href="graph_1.html#E3"><i><font color="Green">Lemma27</font></i></a>, </i>
;<br/><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E9:38"/>
<font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H2</font>
 <b>by </b><i>, , , , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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