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<div class="add">

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

<i><font color="Green">E29</font></i>: the <a href="graph_1.html#U1" target="_self">Vertices</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span> = 
the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">G</font> <a href="xboole_0.html#K2">\/</a> the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">G</font>
<b>by </b><i/>
<br/>.= 
the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">G</font>

;<br/>
<i><font color="Green">E35</font></i>: the <a href="graph_1.html#U2" target="_self">Edges</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span> = 
the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font> <a href="xboole_0.html#K2">\/</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font>
<b>by </b><i/>
<br/>.= 
the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font>

;<br/>
<b>then </b><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">G</font> = 
the <a href="graph_1.html#U2" target="_self">Edges</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E4:45"/>
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="relat_1.html#K1">dom</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">G</font> holds <br/>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="Olive">v</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_4"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:45_4"/>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">G</font>
 ;<br/>

<a NAME="E2:45_4"/><b>then </b>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:45_4"/>
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">v</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E5:45"/><b>then </b><i><font color="Green">E37</font></i>: 
the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span>
 
<b>by </b><i><a class="txt" href="graph_1.html#E4"><i><font color="Green">Lemma28</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>
<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">G</font> = 
the <a href="graph_1.html#U2" target="_self">Edges</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span>
<b>by </b><i><a class="txt" href="graph_1.html#E3"><i><font color="Green">Lemma27</font></i></a>, </i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> the <a href="graph_1.html#U4" target="_self">Target</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E7:45"/>
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="relat_1.html#K1">dom</a> the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">G</font> holds <br/>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="Olive">v</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U4" target="_self">Target</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_6"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:45_6"/>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">G</font>
 ;<br/>

<a NAME="E2:45_6"/><b>then </b>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:45_6"/>
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">v</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U4" target="_self">Target</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:45"/>
<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="txt" href="graph_1.html#E3"><i><font color="Green">Lemma27</font></i></a>, <a class="txt" href="graph_1.html#E1:45"><i><font color="Green">E29</font></i></a>, <a class="ref" href="graph_1.html#D2" target="_self">Def2</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
