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<b>let </b><font color="Maroon" title="c1">G1</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">G2</font> be    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G1</font>;<br/><b>let </b><font color="Maroon" title="c3">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="168_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:168_1"/><i><font color="Green" title="E68">A1</font></i>: 
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K19" title="GLIB_000:func.19">.edgesInto</a> <font color="Maroon" title="c3">X</font>
 ;<br/><a NAME="E2:168_1"/><b>then </b><i><font color="Green" title="E69">A2</font></i>: 
( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D28" target="_self" title="GLIB_000:def.28">Def28</a></i>;<br/><a NAME="E3:168_1"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>
 <b>by </b><i><a class="txt" href="glib_000.html#E1:168_1"><i><font color="Green" title="E68">A1</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self" title="GLIB_000:def.34">Def34</a></i>;<br/><b>hence </b><a NAME="E4:168_1"/>
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K19" title="GLIB_000:func.19">.edgesInto</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="glib_000.html#E2:168_1"><i><font color="Green" title="E69">A2</font></i></a>, <a class="ref" href="glib_000.html#D28" target="_self" title="GLIB_000:def.28">Def28</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:168"/><i><font color="Green" title="E68">A3</font></i>: 
<font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K19" title="GLIB_000:func.19">.edgesInto</a> <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K19" title="GLIB_000:func.19">.edgesInto</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="168_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:168_2"/><i><font color="Green" title="E69">A4</font></i>: 
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K20" title="GLIB_000:func.20">.edgesOutOf</a> <font color="Maroon" title="c3">X</font>
 ;<br/><a NAME="E2:168_2"/><b>then </b><i><font color="Green" title="E70">A5</font></i>: 
( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D29" target="_self" title="GLIB_000:def.29">Def29</a></i>;<br/><a NAME="E3:168_2"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>
 <b>by </b><i><a class="txt" href="glib_000.html#E1:168_2"><i><font color="Green" title="E69">A4</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self" title="GLIB_000:def.34">Def34</a></i>;<br/><b>hence </b><a NAME="E4:168_2"/>
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K20" title="GLIB_000:func.20">.edgesOutOf</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="glib_000.html#E2:168_2"><i><font color="Green" title="E70">A5</font></i></a>, <a class="ref" href="glib_000.html#D29" target="_self" title="GLIB_000:def.29">Def29</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:168"/><i><font color="Green" title="E69">A6</font></i>: 
<font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K20" title="GLIB_000:func.20">.edgesOutOf</a> <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K20" title="GLIB_000:func.20">.edgesOutOf</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>

<a NAME="E5:168"/><i><font color="Green" title="E70">A7</font></i>: 
<font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K19" title="GLIB_000:func.19">.edgesInto</a> <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesInOut</a> <font color="Maroon" title="c3">X</font>
 
<b>by </b><i><a class="txt" href="glib_000.html#E2:168"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="xboole_1.html#T10" title="XBOOLE_1:th.10">XBOOLE_1:10</a></i>;<br/>
<a NAME="E6:168"/>
<font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K20" title="GLIB_000:func.20">.edgesOutOf</a> <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesInOut</a> <font color="Maroon" title="c3">X</font>
 
<b>by </b><i><a class="txt" href="glib_000.html#E4:168"><i><font color="Green" title="E69">A6</font></i></a>, <a class="ref" href="xboole_1.html#T10" title="XBOOLE_1:th.10">XBOOLE_1:10</a></i>;<br/>
<b>hence </b><a NAME="E7:168"/>
<font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesInOut</a> <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesInOut</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="glib_000.html#E5:168"><i><font color="Green" title="E70">A7</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>

<b>thus </b><a NAME="E8:168"/>
<font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="glib_000.html#E2:168"><i><font color="Green" title="E68">A3</font></i></a>, <a class="txt" href="glib_000.html#E4:168"><i><font color="Green" title="E69">A6</font></i></a>, <a class="ref" href="xboole_1.html#T27" title="XBOOLE_1:th.27">XBOOLE_1:27</a></i>;<br/>


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