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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:10_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:10_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1" target="_self">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" target="_self">Def7</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:10_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" target="_self">Def1</a></i>;<br/><b>take </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font>;<br/><b>thus </b><a NAME="E5:10_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="xboole_0.html#E4:10_1"><i><font color="Green">E8</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E2:10"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:10"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1" target="_self">{}</a> 
 
<b>by </b><i><a class="txt" href="xboole_0.html#E2:10"><i><font color="Green">E8</font></i></a>, <a class="ref" href="xboole_0.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E4:10"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" target="_self">Def7</a></i>;<br/>


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