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<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">G2</font> be    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="170_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:170_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G2</font> <a href="glib_000.html#K23" target="_self">.edgesBetween</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>
 ;<br/><a NAME="E2:170_1"/><b>then </b>
<font color="Maroon">x</font> <a href="glib_000.html#R3" target="_self">SJoins</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">G2</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E3:170_1"/><b>then </b>
<font color="Maroon">x</font> <a href="glib_000.html#R3" target="_self">SJoins</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">G1</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:170_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G1</font> <a href="glib_000.html#K23" target="_self">.edgesBetween</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:170"/>
<font color="Maroon">G2</font> <a href="glib_000.html#K23" target="_self">.edgesBetween</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G1</font> <a href="glib_000.html#K23" target="_self">.edgesBetween</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>
 <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="170_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:170_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G2</font> <a href="glib_000.html#K24" target="_self">.edgesDBetween</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>
 ;<br/><a NAME="E2:170_2"/><b>then </b>
<font color="Maroon">x</font> <a href="glib_000.html#R4" target="_self">DSJoins</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">G2</font>
 <b>by </b><i/>;<br/><a NAME="E3:170_2"/><b>then </b>
<font color="Maroon">x</font> <a href="glib_000.html#R4" target="_self">DSJoins</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">G1</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:170_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G1</font> <a href="glib_000.html#K24" target="_self">.edgesDBetween</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:170"/>
<font color="Maroon">G2</font> <a href="glib_000.html#K24" target="_self">.edgesDBetween</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G1</font> <a href="glib_000.html#K24" target="_self">.edgesDBetween</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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