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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="E1:103"/><i><font color="Green">E62</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> or <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R4" target="_self">overlaps</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:103_1"/>
( <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> or <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R4" target="_self">overlaps</a> <font color="Maroon">c<sub>4</sub></font> )
 </span><b>by </b><i><a class="txt" href="pboole.html#E1:103"><i><font color="Green">E62</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1"><b>suppose </b></a><a NAME="E1:103_1_1"/>
<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>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:103_1_1"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="pboole.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E4:103_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="pboole.html#E3:103_1_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="pboole.html#T7" target="_self">Th7</a></i>;<br/><b>hence </b><a NAME="E5:103_1_1"/>
<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#K2" target="_self">\/</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="pboole.html#T10" target="_self">Th10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_2"><b>suppose </b></a><a NAME="E1:103_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R4" target="_self">overlaps</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:103_1_2"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="pboole.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E4:103_1_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1" target="_self">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="pboole.html#E3:103_1_2"><i><font color="Green">E63</font></i></a>, <a class="ref" href="pboole.html#T7" target="_self">Th7</a></i>;<br/><b>hence </b><a NAME="E5:103_1_2"/>
<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#K2" target="_self">\/</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="pboole.html#T10" target="_self">Th10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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