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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:111"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R4" target="_self">overlaps</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D10" target="_self">PBOOLE:def 10</a><br/>

<b>assume </b><a NAME="E2:111"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:111"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="pboole.html#E1:111"><i><font color="Green">E65</font></i></a>, <a class="ref" href="pboole.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E4:111"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="pboole.html#E2:111"><i><font color="Green">E66</font></i></a>, <a class="ref" href="pboole.html#D9" target="_self">Def9</a></i>;<br/>
<a NAME="E5:111"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T81">XBOOLE_1:81</a></i>;<br/>
<b>hence </b><a NAME="E6:111"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="pboole.html#E2:111"><i><font color="Green">E66</font></i></a>, <a class="ref" href="pboole.html#D9" target="_self">Def9</a></i>;<br/>


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