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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:171"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="171_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:171_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> 
 ;<br/><a NAME="E2:171_1"/><b>then </b><i><font color="Green">E72</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E52"><i><font color="Green">Lemma33</font></i></a></i>;<br/><a NAME="E3:171_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="glib_000.html#E1:171"><i><font color="Green">E71</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self">Def34</a></i>;<br/><b>hence </b><a NAME="E4:171_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> 
 <b>by </b><i><a class="txt" href="glib_000.html#E2:171_1"><i><font color="Green">E72</font></i></a>, <a class="txt" href="glib_000.html#E52"><i><font color="Green">Lemma33</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:171"/>
<font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="171_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:171_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> 
 ;<br/><a NAME="E2:171_2"/><b>then </b><i><font color="Green">E72</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E53"><i><font color="Green">Lemma34</font></i></a></i>;<br/><a NAME="E3:171_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="glib_000.html#E1:171"><i><font color="Green">E71</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self">Def34</a></i>;<br/><b>hence </b><a NAME="E4:171_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> 
 <b>by </b><i><a class="txt" href="glib_000.html#E2:171_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="glib_000.html#E53"><i><font color="Green">Lemma34</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:171"/>
<font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="171_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:171_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a> 
 ;<br/><a NAME="E2:171_3"/><b>then </b><i><font color="Green">E72</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> or <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> ) )
 <b>by </b><i><a class="ref" href="glib_000.html#T64" target="_self">Th64</a></i>;<br/><a NAME="E3:171_3"/><b>then </b>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E1:171"><i><font color="Green">E71</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self">Def34</a></i>;<br/><b>hence </b><a NAME="E4:171_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a> 
 <b>by </b><i><a class="txt" href="glib_000.html#E2:171_3"><i><font color="Green">E72</font></i></a>, <a class="ref" href="glib_000.html#T64" target="_self">Th64</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:171"/>
<font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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