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<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:51"/><i><font color="Green" title="E29">A1</font></i>: 
 <a href="setfam_1.html#K2" title="SETFAM_1:func.2">UNION</a> <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>assume </b><a NAME="E2:51"/><i><font color="Green" title="E30">A2</font></i>: 
( <font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:51"/><i><font color="Green" title="E31">A3</font></i>: 
<font color="Maroon" title="c3">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">Y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:51"/><i><font color="Green" title="E32">A4</font></i>: 
<font color="Maroon" title="c4">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="txt" href="topgen_4.html#E2:51"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E7:51"/>
<font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K2" title="SETFAM_1:func.2">UNION</a> <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">G</font>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E4:51"><i><font color="Green" title="E31">A3</font></i></a>, <a class="txt" href="topgen_4.html#E6:51"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="setfam_1.html#D4" title="SETFAM_1:def.4">SETFAM_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E8:51"/>
contradiction
 <b>by </b><i><a class="txt" href="topgen_4.html#E1:51"><i><font color="Green" title="E29">A1</font></i></a></i>;<br/>


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