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<b>let </b><font color="Maroon">G1</font> be  <a href="graph_1.html#V1" target="_self">strict</a> <a href="graph_1.html#NM1">Graph</a>, <font color="Maroon">G2</font> be  <a href="graph_1.html#V1" target="_self">strict</a> <a href="graph_1.html#NM1">Graph</a>;<br/>

<b>assume </b><a NAME="E1:68"/><i><font color="Green">E29</font></i>: 
( the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">G1</font> <a href="partfun1.html#R1">tolerates</a> the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">G2</font> &amp; the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">G1</font> <a href="partfun1.html#R1">tolerates</a> the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">G2</font> )
 ;<br/>

<b>assume </b><a NAME="E2:68"/><i><font color="Green">E35</font></i>: 
 <a href="graph_1.html#K7" target="_self">bool</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="graph_1.html#K7" target="_self">bool</a> <font color="Maroon">G1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="graph_1.html#K7" target="_self">bool</a> <font color="Maroon">G2</font></span>)</span>
 ;<br/>

<a NAME="E3:68"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font> <a href="hidden.html#R2">in</a>  <a href="graph_1.html#K7" target="_self">bool</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font></span>)</span>
 
<b>by </b><i/>;<br/>
<div><i><font color="Green">E37</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:68_1"/>
<font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font> <a href="hidden.html#R2">in</a>  <a href="graph_1.html#K7" target="_self">bool</a> <font color="Maroon">G1</font>
 ;<br/><a NAME="E2:68_1"/><b>then </b>
<font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font> is    <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">G1</font>
 <b>by </b><i/>;<br/><a NAME="E3:68_1"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font> <a href="graph_1.html#R4" target="_self">c=</a> <font color="Maroon">G1</font>
 <b>by </b><i/>;<br/><a NAME="E4:68_1"/>
<font color="Maroon">G1</font> <a href="graph_1.html#R4" target="_self">c=</a> <font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font>
 <b>by </b><i>, </i>;<br/><a NAME="E5:68_1"/><b>then </b>
<font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G1</font>
 <b>by </b><i>, <a class="ref" href="graph_1.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E6:68_1"/>
<font color="Maroon">G2</font> <a href="graph_1.html#R4" target="_self">c=</a> <font color="Maroon">G1</font>
 <b>by </b><i>, <a class="txt" href="graph_1.html#E4:68"><i><font color="Green">E37</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:68_2"/>
<font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font> <a href="hidden.html#R2">in</a>  <a href="graph_1.html#K7" target="_self">bool</a> <font color="Maroon">G2</font>
 ;<br/><a NAME="E2:68_2"/><b>then </b>
<font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font> is    <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">G2</font>
 <b>by </b><i/>;<br/><a NAME="E3:68_2"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font> <a href="graph_1.html#R4" target="_self">c=</a> <font color="Maroon">G2</font>
 <b>by </b><i/>;<br/><a NAME="E4:68_2"/>
<font color="Maroon">G2</font> <a href="graph_1.html#R4" target="_self">c=</a> <font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font>
 <b>by </b><i><a class="txt" href="graph_1.html#E3:68_2"><i><font color="Green">E39</font></i></a>, </i>;<br/><a NAME="E5:68_2"/><b>then </b>
<font color="Maroon">G1</font> <a href="graph_1.html#K1" target="_self">\/</a> <font color="Maroon">G2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G2</font>
 <b>by </b><i>, <a class="ref" href="graph_1.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E6:68_2"/>
<font color="Maroon">G1</font> <a href="graph_1.html#R4" target="_self">c=</a> <font color="Maroon">G2</font>
 <b>by </b><i><a class="txt" href="graph_1.html#E3:68_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="graph_1.html#E4:68"><i><font color="Green">E37</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:68"/>
( <font color="Maroon">G1</font> <a href="graph_1.html#R4" target="_self">c=</a> <font color="Maroon">G2</font> or <font color="Maroon">G2</font> <a href="graph_1.html#R4" target="_self">c=</a> <font color="Maroon">G1</font> )
 <b>by </b><i>, , , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


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