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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">H</font> be    <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">G</font>;<br/>



<b>set </b><font color="Maroon">EH</font> = the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H</font>;<br/>
<b>set </b><font color="Maroon">VH</font> = the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H</font>;<br/>
<b>set </b><font color="Maroon">EG</font> = the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font>;<br/>
<b>set </b><font color="Maroon">VG</font> = the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">G</font>;<br/>
<a NAME="E1:40"/>
( the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font> &amp; the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a> the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">G</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:40"/><b>then </b>
(  <a href="funct_2.html#K1">Funcs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H</font>,the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a>  <a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H</font>,the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H</font> &amp;  <a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H</font>,the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a>  <a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font>,the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">G</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T141">FUNCT_2:141</a>, <a class="ref" href="partfun1.html#T128">PARTFUN1:128</a></i>;<br/>
<a NAME="E3:40"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="funct_2.html#K1">Funcs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H</font>,the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a>  <a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font>,the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:40"/><i><font color="Green">E35</font></i>: 
the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E5:40"/><b>then </b>
the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">H</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H</font>,the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T11">FUNCT_2:11</a></i>;<br/>
<b>hence </b><a NAME="E6:40"/>
the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">H</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font>,the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">G</font>
 <b>by </b><i/>;<br/>

<a NAME="E7:40"/>
the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">H</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">H</font>,the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">H</font>
 
<b>by </b><i>, <a class="ref" href="funct_2.html#T11">FUNCT_2:11</a></i>;<br/>
<b>hence </b><a NAME="E8:40"/>
the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">H</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">G</font>,the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">G</font>
 <b>by </b><i/>;<br/>


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